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Deck 7: Exponential Functions
ملء الشاشة (f)
سؤال
Find the domain on which 
is one-to-one and a formula for the inverse of 
.
is one-to-one and a formula for the inverse of .
سؤال
Calculate 
where 
is the inverse of 
:
A)
B)
where is the inverse of : A)
B)
سؤال
Let 
with domain 
. Find 
with domain . Find سؤال
Evaluate the integrals:
A)
B)
C)
A)
B)
C)
سؤال
Solve: 
سؤال
Find the derivative of the function at the given point:
A)
B)
C)
A)
B)
C)
سؤال
Solve 
سؤال
Find 
and 
, such that 
is tangent to 
at 
.
and , such that is tangent to at . سؤال
Find the slope of the function 
at 
.
at . سؤال
Calculate 
where 
is the inverse of 
:
A)
B)
where is the inverse of : A)
B)
سؤال
Use the definition of the derivative at 
to find 
if 
.
to find if . سؤال
Let 
be the inverse of 
. Use the geometric relation between the graphs of inverse functions to compute the integral 
. 
be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral . سؤال
Let 
be the inverse of 
. Use the geometric relation between the graphs of inverse functions to compute the integral 
. 
be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral . سؤال
Compute the integral 
.
. سؤال
Let 
be the inverse of 
.
Use the geometric relation between the graphs of inverse functions to compute the integral
. 
be the inverse of .Use the geometric relation between the graphs of inverse functions to compute the integral
. سؤال
Solve: 
سؤال
Calculate 
where 
is the inverse of 
:
A)
B)
where is the inverse of : A)
B)
سؤال
Solve: 
سؤال
Calculate 
where 
is the inverse of 
:
A)
B)
where is the inverse of : A)
B)
سؤال
Let 
be the inverse of 
. Use the geometric relation between the graphs of inverse functions to compute the integral 
. 
be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral . سؤال
Let 
. Use logarithmic differentiation to calculate 
.
. Use logarithmic differentiation to calculate . سؤال
The derivative of 
is
A)
B)
C)
D)
E)
isA)
B)
C)
D)
E)
سؤال
سؤال
Find an equation of the tangent line to the graph of the function 
for 
.
for . سؤال
Let 
. Calculate 
.
. Calculate . سؤال
Evaluate the integrals:
A)
B)
A)
B)
سؤال
The population of a country was 
in 1980, whereas in 1990 it was 
A) Find the population in
B) Determine the population's doubling time.
Assume that the rate of growth is proportional to the population.
in 1980, whereas in 1990 it was A) Find the population in
B) Determine the population's doubling time.
Assume that the rate of growth is proportional to the population.
سؤال
Find the slope of the tangent line to the graph of the function 
at 
To find 
, use the equality 
or use a calculator.
at To find , use the equality or use a calculator. سؤال
The rate of change of the following function is proportional to 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
سؤال
Evaluate the integrals using the given substitutions:
A)
B)
A)
B)
سؤال
Consider the Gompertz differential equation 
.
Define the function
by 
. The differential equation for 
is,
A)
B)
C)
D)
E)
.Define the function
by . The differential equation for is,A)
B)
C)
D)
E)
سؤال
Evaluate the definite integrals:
A)
B)
C)
A)
B)
C)
سؤال
Let 
. Use logarithmic differentiation to calculate 
.
. Use logarithmic differentiation to calculate . سؤال
A population is modeled by a function 
. Initially, the population counts 1000. The rate of change of the population is proportional to 
. Find the population at time 
years given that the doubling time is 8 years.
. Initially, the population counts 1000. The rate of change of the population is proportional to . Find the population at time years given that the doubling time is 8 years. سؤال
The population of a country was 
in 
and 
in 
. The population doubling time is:
A) 25 years
B) 30.1 years
C) 39.5 years
D) 40.1 years
E) none of the above
in and in . The population doubling time is:A) 25 years
B) 30.1 years
C) 39.5 years
D) 40.1 years
E) none of the above
سؤال
Find 
if 
.
if . سؤال
Compute the derivatives of the following functions:
A)
B)
C)
A)
B)
C)
سؤال
Find all solutions to 
satisfying 
.
satisfying . سؤال
Let 
. Calculate 
.
. Calculate . سؤال
Evaluate the integrals:
A)
B)
C)
A)
B)
C)
سؤال
How long will it take for your money to double when it is invested at an annual rate of 
and compounded yearly? How long will it take for your money to double at an annual rate of 
?
and compounded yearly? How long will it take for your money to double at an annual rate of ? سؤال
A glass of cold water with initial temperature 
C is placed in a room held at 
C. If the temperature of the water is 
C after 1 h, what will the temperature of the water be after another hour?
C is placed in a room held at C. If the temperature of the water is C after 1 h, what will the temperature of the water be after another hour? سؤال
سؤال
A frozen turkey with an initial temperature of 
F is placed into a hot oven. After 1 h, the temperature of the turkey is 
F. After 3 h, the temperature is 
F. What is the temperature of the oven?
F is placed into a hot oven. After 1 h, the temperature of the turkey is F. After 3 h, the temperature is F. What is the temperature of the oven? سؤال
David has 
in his account earning interest at an annual rate of 
compounded weekly. How much money was in his account 2 years ago (1 year = 52 weeks)?
in his account earning interest at an annual rate of compounded weekly. How much money was in his account 2 years ago (1 year = 52 weeks)? سؤال
Bob deposits 
to a bank account with an annual interest rate of 
. The interest is compounded continuously. How much money will Bob earn after 5 years?
A)
B)
C)
D)
E) $1516
to a bank account with an annual interest rate of . The interest is compounded continuously. How much money will Bob earn after 5 years?A)
B)
C)
D)
E) $1516
سؤال
سؤال
At 6:45 a.m., a glass of cold water with initial temperature 
C is placed in a room held at 
C. If the temperature of the water is 
C at 8:15 a.m., when will the water temperature reach 
C?
C is placed in a room held at C. If the temperature of the water is C at 8:15 a.m., when will the water temperature reach C? سؤال
A frozen turkey with an initial temperature of 
C is placed into a hot oven held at 
C. After 1 h, the temperature of the turkey has risen to 
C. Give an equation representing the temperature of the turkey as a function of 
, the number of hours since the turkey was placed in the oven.
C is placed into a hot oven held at C. After 1 h, the temperature of the turkey has risen to C. Give an equation representing the temperature of the turkey as a function of , the number of hours since the turkey was placed in the oven. سؤال
By Newton's Law of Cooling, an object in air cools down at a rate proportional to the difference between the object's temperature and the air temperature. When the air temperature is 
C, it takes 10 min for the object to cool down from 
C to 
C. The temperature of the object decreases from 
C to 
C during:
A) 30.21 min
B) 22.37 min
C) 16.67 min
D) 19.10 min
E) 6.66 min
C, it takes 10 min for the object to cool down from C to C. The temperature of the object decreases from C to C during:A) 30.21 min
B) 22.37 min
C) 16.67 min
D) 19.10 min
E) 6.66 min
سؤال
is deposited into an account earning interest at an annual rate of 
. Find the value of the account after one year if A) it is compounded twice a year.
B) it is compounded monthly.
C) it is compounded weekly (52 weeks a year)
D) it is compounded daily (365 days a year)
E) it is compounded continuously.
Does the method of compounding have much effect on the final value?
سؤال
Ben has 
in his account earning interest at an annual rate of 
compounded monthly. How much money was in his account 3 years ago?
in his account earning interest at an annual rate of compounded monthly. How much money was in his account 3 years ago? سؤال
سؤال
Find all solutions to 
satisfying 
.
satisfying . سؤال
سؤال
سؤال
The decay constant of a 15-kg isotope is 0.137 (years) 
. Find the half-life of the isotope.
. Find the half-life of the isotope. سؤال
How long will it take for your money to double when it is invested at an annual rate of 
and compounded yearly? How long will it take for your money to double at an annual rate of 
?
and compounded yearly? How long will it take for your money to double at an annual rate of ? سؤال
سؤال
A cold chicken with an initial temperature of 
C is placed in an oven held at 
C. If the temperature of the chicken is 
C after 10 min, how much longer after that must the chicken remain in the oven before it reaches 
C?
C is placed in an oven held at C. If the temperature of the chicken is C after 10 min, how much longer after that must the chicken remain in the oven before it reaches C? سؤال
At 7:00 a.m., a mug of hot chocolate with initial temperature of 
C is placed on a table in a room held at 
C. At 7:45 a.m., the temperature of the hot chocolate is 
C. Express the temperature of the hot chocolate as a function of 
, the number of hours since 7:00 a.m.
C is placed on a table in a room held at C. At 7:45 a.m., the temperature of the hot chocolate is C. Express the temperature of the hot chocolate as a function of , the number of hours since 7:00 a.m. سؤال
Apply L'Hopital's Rule to evaluate the limit
A)
B)
C)
A)
B)
C)
سؤال
A 3-kg object is dropped from a tall building. After 1 s, the object has a velocity of 
m/s. What is the object's terminal velocity?
m/s. What is the object's terminal velocity? سؤال
Compute the following limits:
A)
B)
A)
B)
سؤال
The values of 
and 
, such that the function 
is continuous for all 
are
A)
B)
C)
D)
E)
and , such that the function is continuous for all areA)
B)
C)
D)
E)
سؤال
A 2-kg object is dropped from a height of 75 m. After 1 s, the object has a velocity of 
m/s. What is its velocity after 2 s?
m/s. What is its velocity after 2 s? سؤال
A 1-kg object is dropped from a height of 80 m. After 2 s, the velocity of the object is 
m/s. How long after the ball was dropped did the object have a velocity of 
m/s?
m/s. How long after the ball was dropped did the object have a velocity of m/s? سؤال
Evaluate the limits using L'Hopital's Rule
A)
B)
C)
A)
B)
C)
سؤال
Find the limits using L'Hopital's Rule
A)
B)
A)
B)
سؤال
A mug of hot chocolate with initial temperature 
C is placed on a table in a room held at a constant temperature. After 20 min, the temperature of the hot chocolate is 
C. After another 20 min, the temperature of the hot chocolate is 
C. What is the temperature of the room?
C is placed on a table in a room held at a constant temperature. After 20 min, the temperature of the hot chocolate is C. After another 20 min, the temperature of the hot chocolate is C. What is the temperature of the room? سؤال
Find the horizontal asymptote(s) of the function 
.
. سؤال
From the top of a tall building, a 2-kg object is thrown vertically downward. One second after being thrown, the object has a velocity of 
m/s. If the coefficient of air resistance is 
kg/s, what was the initial velocity of the object?
m/s. If the coefficient of air resistance is kg/s, what was the initial velocity of the object? سؤال
A glass of cold water with initial temperature 
C is placed in a room held at a constant temperature. After 1 h, the water temperature is 
C. After another 2 h, the water temperature is 
C. What is the temperature of the room?
C is placed in a room held at a constant temperature. After 1 h, the water temperature is C. After another 2 h, the water temperature is C. What is the temperature of the room? سؤال
From the top of a tall building, a 5-kg object is thrown vertically downward. One second after it is thrown, the object has a velocity of 
m/s. Two seconds after it is thrown, the object has a velocity of 
m/s. What was the initial velocity of the object?
m/s. Two seconds after it is thrown, the object has a velocity of m/s. What was the initial velocity of the object? سؤال
Find the horizontal asymptote(s) of the function 
.
. سؤال
From the top of a tall building, a 1-kg object is thrown vertically downward. One second after being thrown, the object has a velocity of 
m/s. Two seconds after being thrown, the object has a velocity of 
m/s. What is the coefficient of air resistance 
?
m/s. Two seconds after being thrown, the object has a velocity of m/s. What is the coefficient of air resistance ? سؤال
A mug of hot chocolate with initial temperature 
is placed on a table in a room held at 
C. After 15 min, the temperature of the hot chocolate is 
C. After an additional 30 min, the temperature of the hot chocolate is 
C. What was the initial temperature 
?
is placed on a table in a room held at C. After 15 min, the temperature of the hot chocolate is C. After an additional 30 min, the temperature of the hot chocolate is C. What was the initial temperature ? سؤال
At 7:30 a.m., a mug of hot chocolate with initial temperature of 
C is placed on a table in a room held at 
C. At 8:45 a.m., the temperature of the hot chocolate is 
C. At what time did the temperature of the hot chocolate reach 
C?
C is placed on a table in a room held at C. At 8:45 a.m., the temperature of the hot chocolate is C. At what time did the temperature of the hot chocolate reach C? سؤال
Evaluate the limits using L'Hopital's Rule
A)
B)
C)
A)
B)
C)
سؤال
A mug of hot chocolate with initial temperature 
C is in a room held at 
C. After 30 min, the temperature of the hot chocolate is 
C. What is the temperature of the hot chocolate after another 10 min?
C is in a room held at C. After 30 min, the temperature of the hot chocolate is C. What is the temperature of the hot chocolate after another 10 min?
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ملء الشاشة (f)
Deck 7: Exponential Functions
1
Find the domain on which is one-to-one and a formula for the inverse of .
is one-to-one and a formula for the inverse of .
is one-to-one on 
2
Calculate where is the inverse of :
A)
B)
where is the inverse of : A)
B)
A) 
B) 
B) 3
Let with domain . Find
with domain . Find 
4
Evaluate the integrals:
A)
B)
C)
A)
B)
C)
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5
Solve:
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6
Find the derivative of the function at the given point:
A)
B)
C)
A)
B)
C)
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7
Solve
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8
Find and , such that is tangent to at .
and , such that is tangent to at . فتح الحزمة
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9
Find the slope of the function at .
at . فتح الحزمة
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10
Calculate where is the inverse of :
A)
B)
where is the inverse of : A)
B)
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11
Use the definition of the derivative at to find if .
to find if . فتح الحزمة
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12
Let be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral .
be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral . فتح الحزمة
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13
Let be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral .
be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral . فتح الحزمة
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14
Compute the integral .
. فتح الحزمة
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15
Let be the inverse of .
Use the geometric relation between the graphs of inverse functions to compute the integral .
be the inverse of .Use the geometric relation between the graphs of inverse functions to compute the integral
. فتح الحزمة
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16
Solve:
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17
Calculate where is the inverse of :
A)
B)
where is the inverse of : A)
B)
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18
Solve:
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19
Calculate where is the inverse of :
A)
B)
where is the inverse of : A)
B)
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20
Let be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral .
be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral . فتح الحزمة
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21
Let . Use logarithmic differentiation to calculate .
. Use logarithmic differentiation to calculate . فتح الحزمة
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22
The derivative of is
A)
B)
C)
D)
E)
isA)
B)
C)
D)
E)
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23
The population in a certain country was 10,900,000 in 1990 and 17,100,000 in 2005. The doubling time of the population is:
A) 52.7 years
B) 53.6 years
C) 31.3 years
D) 23.1 years
E) none of the above
A) 52.7 years
B) 53.6 years
C) 31.3 years
D) 23.1 years
E) none of the above
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24
Find an equation of the tangent line to the graph of the function for .
for . فتح الحزمة
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25
Let . Calculate .
. Calculate . فتح الحزمة
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26
Evaluate the integrals:
A)
B)
A)
B)
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27
The population of a country was in 1980, whereas in 1990 it was
A) Find the population in
B) Determine the population's doubling time.
Assume that the rate of growth is proportional to the population.
in 1980, whereas in 1990 it was A) Find the population in
B) Determine the population's doubling time.
Assume that the rate of growth is proportional to the population.
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28
Find the slope of the tangent line to the graph of the function at To find , use the equality or use a calculator.
at To find , use the equality or use a calculator. فتح الحزمة
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29
The rate of change of the following function is proportional to .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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30
Evaluate the integrals using the given substitutions:
A)
B)
A)
B)
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31
Consider the Gompertz differential equation .
Define the function by . The differential equation for is,
A)
B)
C)
D)
E)
.Define the function
by . The differential equation for is,A)
B)
C)
D)
E)
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32
Evaluate the definite integrals:
A)
B)
C)
A)
B)
C)
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33
Let . Use logarithmic differentiation to calculate .
. Use logarithmic differentiation to calculate . فتح الحزمة
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34
A population is modeled by a function . Initially, the population counts 1000. The rate of change of the population is proportional to . Find the population at time years given that the doubling time is 8 years.
. Initially, the population counts 1000. The rate of change of the population is proportional to . Find the population at time years given that the doubling time is 8 years. فتح الحزمة
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35
The population of a country was in and in . The population doubling time is:
A) 25 years
B) 30.1 years
C) 39.5 years
D) 40.1 years
E) none of the above
in and in . The population doubling time is:A) 25 years
B) 30.1 years
C) 39.5 years
D) 40.1 years
E) none of the above
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36
Find if .
if . فتح الحزمة
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37
Compute the derivatives of the following functions:
A)
B)
C)
A)
B)
C)
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38
Find all solutions to satisfying .
satisfying . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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39
Let . Calculate .
. Calculate . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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40
Evaluate the integrals:
A)
B)
C)
A)
B)
C)
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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41
How long will it take for your money to double when it is invested at an annual rate of and compounded yearly? How long will it take for your money to double at an annual rate of ?
and compounded yearly? How long will it take for your money to double at an annual rate of ? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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42
A glass of cold water with initial temperature C is placed in a room held at C. If the temperature of the water is C after 1 h, what will the temperature of the water be after another hour?
C is placed in a room held at C. If the temperature of the water is C after 1 h, what will the temperature of the water be after another hour? فتح الحزمة
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43
A drug leaves a person's bloodstream at a rate proportional to the amount present. Assume that half of the initial amount of the drug is still in the bloodstream 4 hours after the dose was given. When is one-tenth of the initial dose remaining in the bloodstream?
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44
A frozen turkey with an initial temperature of F is placed into a hot oven. After 1 h, the temperature of the turkey is F. After 3 h, the temperature is F. What is the temperature of the oven?
F is placed into a hot oven. After 1 h, the temperature of the turkey is F. After 3 h, the temperature is F. What is the temperature of the oven? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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45
David has in his account earning interest at an annual rate of compounded weekly. How much money was in his account 2 years ago (1 year = 52 weeks)?
in his account earning interest at an annual rate of compounded weekly. How much money was in his account 2 years ago (1 year = 52 weeks)? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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46
Bob deposits to a bank account with an annual interest rate of . The interest is compounded continuously. How much money will Bob earn after 5 years?
A)
B)
C)
D)
E) $1516
to a bank account with an annual interest rate of . The interest is compounded continuously. How much money will Bob earn after 5 years?A)
B)
C)
D)
E) $1516
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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47
How much would a 20-year-old have to invest today in order to have $1 million 30 years from now if the interest is compounded continuously at an annual rate of 6.4%?
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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48
At 6:45 a.m., a glass of cold water with initial temperature C is placed in a room held at C. If the temperature of the water is C at 8:15 a.m., when will the water temperature reach C?
C is placed in a room held at C. If the temperature of the water is C at 8:15 a.m., when will the water temperature reach C? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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49
A frozen turkey with an initial temperature of C is placed into a hot oven held at C. After 1 h, the temperature of the turkey has risen to C. Give an equation representing the temperature of the turkey as a function of , the number of hours since the turkey was placed in the oven.
C is placed into a hot oven held at C. After 1 h, the temperature of the turkey has risen to C. Give an equation representing the temperature of the turkey as a function of , the number of hours since the turkey was placed in the oven. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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50
By Newton's Law of Cooling, an object in air cools down at a rate proportional to the difference between the object's temperature and the air temperature. When the air temperature is C, it takes 10 min for the object to cool down from C to C. The temperature of the object decreases from C to C during:
A) 30.21 min
B) 22.37 min
C) 16.67 min
D) 19.10 min
E) 6.66 min
C, it takes 10 min for the object to cool down from C to C. The temperature of the object decreases from C to C during:A) 30.21 min
B) 22.37 min
C) 16.67 min
D) 19.10 min
E) 6.66 min
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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51
is deposited into an account earning interest at an annual rate of . Find the value of the account after one year if A) it is compounded twice a year.
B) it is compounded monthly.
C) it is compounded weekly (52 weeks a year)
D) it is compounded daily (365 days a year)
E) it is compounded continuously.
Does the method of compounding have much effect on the final value?
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52
Ben has in his account earning interest at an annual rate of compounded monthly. How much money was in his account 3 years ago?
in his account earning interest at an annual rate of compounded monthly. How much money was in his account 3 years ago? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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53
Bob's retirement account pays about $120,000 per year, continuously for 20 years. Find the present value of the income stream if the interest rate is 5.5%.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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54
Find all solutions to satisfying .
satisfying . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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55
How much money will an investment of $12,000 be worth in 25 years if it is invested in a bank earning 5.3% interest compounded quarterly?
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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56
The population in an ant colony doubles every 3 months. Assuming exponential growth, how many years does it take the population to increase five fold?
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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57
The decay constant of a 15-kg isotope is 0.137 (years) . Find the half-life of the isotope.
. Find the half-life of the isotope. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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58
How long will it take for your money to double when it is invested at an annual rate of and compounded yearly? How long will it take for your money to double at an annual rate of ?
and compounded yearly? How long will it take for your money to double at an annual rate of ? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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k this deck
59
Jane wins the lottery. She has a choice about how to receive her winnings.
Plan A: receive continuous payments of $10,000 a year for the next 20 years.
Plan B: receive $120,000 now and no additional money.
Assume that Jane can earn 6% interest compounded continuously.
A) Compute the present value of the income stream for Plan A.
B) If the yearly amount for Plan A is changed to $10,500, which plan should
Jane use if she bases her decision solely on present value?
Plan A: receive continuous payments of $10,000 a year for the next 20 years.
Plan B: receive $120,000 now and no additional money.
Assume that Jane can earn 6% interest compounded continuously.
A) Compute the present value of the income stream for Plan A.
B) If the yearly amount for Plan A is changed to $10,500, which plan should
Jane use if she bases her decision solely on present value?
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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k this deck
60
A cold chicken with an initial temperature of C is placed in an oven held at C. If the temperature of the chicken is C after 10 min, how much longer after that must the chicken remain in the oven before it reaches C?
C is placed in an oven held at C. If the temperature of the chicken is C after 10 min, how much longer after that must the chicken remain in the oven before it reaches C? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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61
At 7:00 a.m., a mug of hot chocolate with initial temperature of C is placed on a table in a room held at C. At 7:45 a.m., the temperature of the hot chocolate is C. Express the temperature of the hot chocolate as a function of , the number of hours since 7:00 a.m.
C is placed on a table in a room held at C. At 7:45 a.m., the temperature of the hot chocolate is C. Express the temperature of the hot chocolate as a function of , the number of hours since 7:00 a.m. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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62
Apply L'Hopital's Rule to evaluate the limit
A)
B)
C)
A)
B)
C)
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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63
A 3-kg object is dropped from a tall building. After 1 s, the object has a velocity of m/s. What is the object's terminal velocity?
m/s. What is the object's terminal velocity? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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64
Compute the following limits:
A)
B)
A)
B)
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افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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65
The values of and , such that the function is continuous for all are
A)
B)
C)
D)
E)
and , such that the function is continuous for all areA)
B)
C)
D)
E)
فتح الحزمة
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66
A 2-kg object is dropped from a height of 75 m. After 1 s, the object has a velocity of m/s. What is its velocity after 2 s?
m/s. What is its velocity after 2 s? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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67
A 1-kg object is dropped from a height of 80 m. After 2 s, the velocity of the object is m/s. How long after the ball was dropped did the object have a velocity of m/s?
m/s. How long after the ball was dropped did the object have a velocity of m/s? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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68
Evaluate the limits using L'Hopital's Rule
A)
B)
C)
A)
B)
C)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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69
Find the limits using L'Hopital's Rule
A)
B)
A)
B)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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k this deck
70
A mug of hot chocolate with initial temperature C is placed on a table in a room held at a constant temperature. After 20 min, the temperature of the hot chocolate is C. After another 20 min, the temperature of the hot chocolate is C. What is the temperature of the room?
C is placed on a table in a room held at a constant temperature. After 20 min, the temperature of the hot chocolate is C. After another 20 min, the temperature of the hot chocolate is C. What is the temperature of the room? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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71
Find the horizontal asymptote(s) of the function .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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72
From the top of a tall building, a 2-kg object is thrown vertically downward. One second after being thrown, the object has a velocity of m/s. If the coefficient of air resistance is kg/s, what was the initial velocity of the object?
m/s. If the coefficient of air resistance is kg/s, what was the initial velocity of the object? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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73
A glass of cold water with initial temperature C is placed in a room held at a constant temperature. After 1 h, the water temperature is C. After another 2 h, the water temperature is C. What is the temperature of the room?
C is placed in a room held at a constant temperature. After 1 h, the water temperature is C. After another 2 h, the water temperature is C. What is the temperature of the room? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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74
From the top of a tall building, a 5-kg object is thrown vertically downward. One second after it is thrown, the object has a velocity of m/s. Two seconds after it is thrown, the object has a velocity of m/s. What was the initial velocity of the object?
m/s. Two seconds after it is thrown, the object has a velocity of m/s. What was the initial velocity of the object? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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75
Find the horizontal asymptote(s) of the function .
. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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76
From the top of a tall building, a 1-kg object is thrown vertically downward. One second after being thrown, the object has a velocity of m/s. Two seconds after being thrown, the object has a velocity of m/s. What is the coefficient of air resistance ?
m/s. Two seconds after being thrown, the object has a velocity of m/s. What is the coefficient of air resistance ? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
k this deck
77
A mug of hot chocolate with initial temperature is placed on a table in a room held at C. After 15 min, the temperature of the hot chocolate is C. After an additional 30 min, the temperature of the hot chocolate is C. What was the initial temperature ?
is placed on a table in a room held at C. After 15 min, the temperature of the hot chocolate is C. After an additional 30 min, the temperature of the hot chocolate is C. What was the initial temperature ? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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78
At 7:30 a.m., a mug of hot chocolate with initial temperature of C is placed on a table in a room held at C. At 8:45 a.m., the temperature of the hot chocolate is C. At what time did the temperature of the hot chocolate reach C?
C is placed on a table in a room held at C. At 8:45 a.m., the temperature of the hot chocolate is C. At what time did the temperature of the hot chocolate reach C? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
k this deck
79
Evaluate the limits using L'Hopital's Rule
A)
B)
C)
A)
B)
C)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
فتح الحزمة
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80
A mug of hot chocolate with initial temperature C is in a room held at C. After 30 min, the temperature of the hot chocolate is C. What is the temperature of the hot chocolate after another 10 min?
C is in a room held at C. After 30 min, the temperature of the hot chocolate is C. What is the temperature of the hot chocolate after another 10 min? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
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فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 106 في هذه المجموعة.
