Question 1

Find all numbers x such that e²^x + e^x = 20. Round the answer to 4 decimal places.

Accepted Answer

The answer of Find all numbers x such that e²^x...

Question 2

What is the area of the region under the curve , above the x-axis, and between the lines x = 1 and x = e¹¹.

Accepted Answer

The answer of What is the area of the region...

Question 3

Given that 2¹⁰$\approx$ 10³, find the value of A such that .

Accepted Answer

The answer of Given that 2¹⁰$\approx$ 10³, find the value...

Question 4

Given that 2¹⁰ $\approx$10³, determine which of the two numbers is larger.

Accepted Answer

The answer of Given that 2¹⁰ $\approx$10³, determine which of...

Question 5

Without using a calculator or computer, give a rough estimate of   .
A)
 
B)
 
C)
 
D)

Accepted Answer

The answer of Without using a calculator or computer, give...

Question 6

Without using a calculator or computer, determine which of the two numbers  is larger.
A)  is larger than  
B)  is larger than  
C) They are equal to each other
D) Cannot be determined

Accepted Answer

The answer of Without using a calculator or computer, determine...

Question 7

Suppose that you deposit into a savings account one dime on January 1, two dimes on January 2, four dines on January 3, and so on, doubling the amount of your deposit each day. After how many days, will your daily deposit exceed $100,000,000?

Accepted Answer

The answer of Suppose that you deposit into a savings...

Question 8

Suppose that you deposit into a savings account one cent on January 1, five cents on January 2, twenty five cents on January 3, and so on, quintupling the amount of your deposit each day. What is the first day that your daily deposit will exceed $10,000?
A) January 6
B) January 7
C) January 8
D) January 9

Accepted Answer

The deposit amount follows a geometric progression with the first term as $0.01 and a common ratio of 5. The formula for the nth term is $ a_n = 0.01 \times 5^{(n-1)} $. Solving for $ a_n > 10000 $, we find that on January 9 (n=9), the deposit exceeds $10,000.

Question 9

Suppose that a colony of bacteria starts with 50 cells and quadruples in size every 3 hours. Approximately how many cells will be in the colony after 2 hours?
A) 126
B) 800
C) 123
D) 3,200

Accepted Answer

After 3 hours, the colony will have 50 * 4 = 200 cells. After 2 hours, the colony will have approximately 200 / 2 = 100 cells.

Question 10

Suppose $900 is deposited in a bank account paying 1% interest per year, compounded 12 times per year. How much will be in the bank account at the end of 12 years? Round your answer to the nearest cent.

Accepted Answer

The answer of Suppose $900 is deposited in a bank...

Question 11

Suppose $3,200 is deposited in a bank CD account paying 6% interest per year, compounded 2 times per year. How much will be in the CD account at the end of 16 years? Round your answer to the nearest cent.
A) $20,650.84
B) $8,240.26
C) $8,129.13
D) $5,135.06

Accepted Answer

The answer of Suppose $3,200 is deposited in a bank...

Question 12

Suppose that a bank account paying 6% interest per year, compounded 4 times per year, contains $7,733 at the end of 14 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Accepted Answer

The answer of Suppose that a bank account paying 6%...

Question 13

Suppose that a bank account paying 3% interest per year, compounded 3 times per year, contains $44,900 at the end of 15 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.
A) $28,820.43
B) $28,944.55
C) $28,693.57
D) $28,819.60

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt). Solving for P gives P = A / (1 + r/n)^(nt). Here, A = $44,900, r = 0.03, n = 3, t = 15. Plugging these values into the formula gives P ≈ $28,693.57.

Question 14

Suppose a savings account pays 5% interest per year, compounded twice per year. If the savings accounts starts with $700, how many years would it take for the savings account to exceed $4,000?

Accepted Answer

The answer of Suppose a savings account pays 5% interest...

Question 15

Suppose a savings account pays 8% interest per year, compounded 6 times per year. If the savings accounts starts with $1,300, how long would it take for the savings account to exceed $6,800?
A) 20 years
B) 19 years
C) 22 years
D) 21 years

Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Here, $P = 1300$, $r = 0.08$, $n = 6$, and we want to find $t$ such that $A > 6800$. Plugging the values into the formula and solving for $t$, we find that it takes slightly over 20 years for the account to exceed $6,800, thus the closest whole number of years is 21.

Question 16

Suppose a bank wants to advertise that $2,000 deposited in its savings account will grow to $2060 in one year. This bank compounds interest 4 times per year. What annual interest rate must the bank pay? Round your answer to one decimal place.

Accepted Answer

The answer of Suppose a bank wants to advertise that...

Question 17

Suppose a bank wants to advertise that $2,000 deposited in its savings account will double in four years. This bank compounds interest 360 times per year. What annual interest rate must the bank pay?
A) 18.33%
B) 17.33%
C) 69.38%
D) 16.33%

Accepted Answer

The answer of Suppose a bank wants to advertise that...

Question 18

A certain rodent colony of 80 individuals doubles its size every 11 months. How many months would it takes to this colony to reach the critical population of 10,000 individuals?

Accepted Answer

The answer of A certain rodent colony of 80 individuals...

Question 19

is $2^{13,746} < 13,746^{1000}$ correct?

Accepted Answer

Comparing the growth rates of exponential and polynomial functions, the polynomial function $13,746^{1000}$ grows faster than the exponential function $2^{13,746}$, making $2^{13,746} < 13,746^{1000}$ correct.

Question 20

Every function f with exponential growth can be represented by a formula of the form $f(x) = cb^x$ for appropriate choices of c and b.

Accepted Answer

Exponential growth functions are characterized by their constant multiplicative rate of change, and the general form $f(x) = cb^x$ captures this property, where $c$ is the initial value when $x=0$ and $b$ is the base of the exponential function, representing the growth factor.

Quiz 4: Exponential Functions, Logarithms, and E

Find all numbers x such that e²^x + e^x = 20. Round the answer to 4 decimal places.

What is the area of the region under the curve , above the x-axis, and between the lines x = 1 and x = e¹¹.

Given that 2¹⁰ $\approx$ 10³, find the value of A such that $Given that 2<sup>10</sup> \approx 10<sup>3</sup>, find the value of A such that .$ .

Given that 2¹⁰ $\approx$ 10³, determine which of the two numbers $Given that 2<sup>10</sup> \approx 10<sup>3</sup>, determine which of the two numbers is larger.$ is larger.

Without using a calculator or computer, give a rough estimate of .

Without using a calculator or computer, determine which of the two numbers is larger.

Suppose that you deposit into a savings account one dime on January 1, two dimes on January 2, four dines on January 3, and so on, doubling the amount of your deposit each day. After how many days, will your daily deposit exceed $100,000,000?

Suppose that you deposit into a savings account one cent on January 1, five cents on January 2, twenty five cents on January 3, and so on, quintupling the amount of your deposit each day. What is the first day that your daily deposit will exceed $10,000?

Suppose that a colony of bacteria starts with 50 cells and quadruples in size every 3 hours. Approximately how many cells will be in the colony after 2 hours?

Suppose $900 is deposited in a bank account paying 1% interest per year, compounded 12 times per year. How much will be in the bank account at the end of 12 years? Round your answer to the nearest cent.

Suppose $3,200 is deposited in a bank CD account paying 6% interest per year, compounded 2 times per year. How much will be in the CD account at the end of 16 years? Round your answer to the nearest cent.

Suppose that a bank account paying 6% interest per year, compounded 4 times per year, contains $7,733 at the end of 14 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Suppose that a bank account paying 3% interest per year, compounded 3 times per year, contains $44,900 at the end of 15 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Suppose a savings account pays 5% interest per year, compounded twice per year. If the savings accounts starts with $700, how many years would it take for the savings account to exceed $4,000?

Suppose a savings account pays 8% interest per year, compounded 6 times per year. If the savings accounts starts with $1,300, how long would it take for the savings account to exceed $6,800?

Suppose a bank wants to advertise that $2,000 deposited in its savings account will grow to $2060 in one year. This bank compounds interest 4 times per year. What annual interest rate must the bank pay? Round your answer to one decimal place.

Suppose a bank wants to advertise that $2,000 deposited in its savings account will double in four years. This bank compounds interest 360 times per year. What annual interest rate must the bank pay?

A certain rodent colony of 80 individuals doubles its size every 11 months. How many months would it takes to this colony to reach the critical population of 10,000 individuals?

is $2^{13,746} < 13,746^{1000}$ correct?

Every function f with exponential growth can be represented by a formula of the form $f(x) = cb^x$ for appropriate choices of c and b.

Quiz 4: Exponential Functions, Logarithms, and E

Find all numbers x such that e2x + ex = 20. Round the answer to 4 decimal places.

What is the area of the region under the curve , above the x-axis, and between the lines x = 1 and x = e11.

Given that 210 ≈\approx≈ 103, find the value of A such that .

Given that 210 ≈\approx≈ 103, determine which of the two numbers is larger.

Without using a calculator or computer, give a rough estimate of .

Without using a calculator or computer, determine which of the two numbers is larger.

Suppose that you deposit into a savings account one dime on January 1, two dimes on January 2, four dines on January 3, and so on, doubling the amount of your deposit each day. After how many days, will your daily deposit exceed $100,000,000?

Suppose that you deposit into a savings account one cent on January 1, five cents on January 2, twenty five cents on January 3, and so on, quintupling the amount of your deposit each day. What is the first day that your daily deposit will exceed $10,000?

Suppose that a colony of bacteria starts with 50 cells and quadruples in size every 3 hours. Approximately how many cells will be in the colony after 2 hours?

Suppose $900 is deposited in a bank account paying 1% interest per year, compounded 12 times per year. How much will be in the bank account at the end of 12 years? Round your answer to the nearest cent.

Suppose $3,200 is deposited in a bank CD account paying 6% interest per year, compounded 2 times per year. How much will be in the CD account at the end of 16 years? Round your answer to the nearest cent.

Suppose that a bank account paying 6% interest per year, compounded 4 times per year, contains $7,733 at the end of 14 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Suppose that a bank account paying 3% interest per year, compounded 3 times per year, contains $44,900 at the end of 15 years. What was the initial amount deposited in the bank account? Round your answer to the nearest cent.

Suppose a savings account pays 5% interest per year, compounded twice per year. If the savings accounts starts with $700, how many years would it take for the savings account to exceed $4,000?

Suppose a savings account pays 8% interest per year, compounded 6 times per year. If the savings accounts starts with $1,300, how long would it take for the savings account to exceed $6,800?

Suppose a bank wants to advertise that $2,000 deposited in its savings account will grow to $2060 in one year. This bank compounds interest 4 times per year. What annual interest rate must the bank pay? Round your answer to one decimal place.

Suppose a bank wants to advertise that $2,000 deposited in its savings account will double in four years. This bank compounds interest 360 times per year. What annual interest rate must the bank pay?

A certain rodent colony of 80 individuals doubles its size every 11 months. How many months would it takes to this colony to reach the critical population of 10,000 individuals?

is 213,746<13,74610002^{13,746} < 13,746^{1000}213,746<13,7461000 correct?

Every function f with exponential growth can be represented by a formula of the form f(x)=cbxf(x) = cb^xf(x)=cbx for appropriate choices of c and b.

Find all numbers x such that e²^x + e^x = 20. Round the answer to 4 decimal places.

What is the area of the region under the curve , above the x-axis, and between the lines x = 1 and x = e¹¹.

Given that 2¹⁰ $\approx$ 10³, find the value of A such that $Given that 2<sup>10</sup> \approx 10<sup>3</sup>, find the value of A such that .$ .

Given that 2¹⁰ $\approx$ 10³, determine which of the two numbers $Given that 2<sup>10</sup> \approx 10<sup>3</sup>, determine which of the two numbers is larger.$ is larger.

is $2^{13,746} < 13,746^{1000}$ correct?

Every function f with exponential growth can be represented by a formula of the form $f(x) = cb^x$ for appropriate choices of c and b.