Question 1

Solve the problem.
-Find the amount of interest earned on the following deposit: $1,000 at 9% compounded annually for 4 years

Accepted Answer

The interest can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt). Here, P = $1,000, r = 0.09, n = 1, and t = 4. The amount A after 4 years is $1,411.58. The interest earned is A - P = $1,411.58 - $1,000 = $411.58.

Question 2

Solve the problem.
-The purchasing power of a dollar is decreasing at the rate of 6.0% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.81? Round answers to the nearest hundredth.

Accepted Answer

The formula for continuous compounding is $ A = Pe^{rt} $. Here, $ A = 0.81 $, $ P = 1 $, and $ r = -0.06 $. Solving for $ t $ gives $ t = \frac{\ln(0.81)}{-0.06} \approx 3.51 $ years.

Question 3

Solve the problem.
-An economist predicts that the buying power $B ( x )$ of a dollar $x$ years from now will decrease according to the formula $\mathrm { B } ( \mathrm { x } ) = 0.78 ^ { \mathrm { x } }$. How much will today's dollar be worth in 4 years? Round the answer to the nearest cent.

Accepted Answer

To find the value of today's dollar in 4 years, substitute $x = 4$ into the formula: $B(4) = 0.78^4$. Calculating this gives approximately $0.37.

Question 4

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 5

Solve the problem.
-The decay of 608 mg of an isotope is given by A $$A ( t ) = 608 e ^ { - 0.019 t }$$ , where t is time in years. Find the amount left after 50 years.

Accepted Answer

The amount left after 50 years is calculated by substituting t = 50 into the decay formula: A(50) = 608 * e^(-0.019 * 50). This evaluates to approximately 235 mg.

Question 6

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 7

Solve the problem.
-Find the amount of interest earned on the following deposit: $1,000 at 12% compounded annually for 7 years

Accepted Answer

The answer of Solve the problem.
-Find the amount of interest...

Question 8

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 9

Determine from its graph if the function is one-to-one.
-$$f ( x ) = \left\{ \begin{array} { l l } 
- x - 3 , & x < 1 \
5 , & x \geq 1
\end{array} \right.$$

Accepted Answer

The function is not one-to-one because there are two different input values (specifically, any value less than 1 and 1 itself) that are both mapped to the output value of 5. Therefore, there is not a unique output for every input, which is the requirement for a function to be one-to-one.

Question 10

Solve the problem.
-The population of a small country increases according to the functio $$B = 2,400,000 e ^ { 0.05 } t$$ t, where t is measured in years. How many people will the country have after 3 years?

Accepted Answer

To find the population after 3 years, substitute $t = 3$ into the given function: $B = 2,400,000 e^{0.05 \times 3}$. This simplifies to $B = 2,400,000 e^{0.15}$, which calculates to approximately 2,788,402 people.

Question 11

Solve the problem.
-A bacteria colony doubles in 5 hr. How long does it take the colony to triple? Use N $$\mathrm { N } = \mathrm { N } _ { 0 } 2 ^ { \mathrm { t } / \mathrm { T } }$$ , where N0 is the initial number of bacteria and T is the time in hours it takes the colony to double. (Round to the nearest
Hundredth, as necessary.)

Accepted Answer

If the colony doubles in 5 hours, we can use the formula to find the growth rate: 
N = N0 * 2^(t/T) 
where N0 is the initial number of bacteria, t is the time elapsed, and T is the time it takes for the colony to double.
Let N0 = 1 (for simplicity)
If the colony doubles in 5 hours, then T = 5.
So, after t hours, the number of bacteria is: 
N = 1 * 2^(t/5)
To find the time it takes for the colony to triple, we need to solve for t when N = 3: 
3 = 1 * 2^(t/5) 
2^(t/5) = 3 
t/5 = log2(3) 
t = 5*log2(3)
t ≈ 7.92 hours 
Therefore, the answer is C.

Question 12

Determine from its graph if the function is one-to-one.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x + 5 , & x > 0 \
4 , & x \leq 0
\end{array} \right.$$

Accepted Answer

The function is not one-to-one because for all $x \leq 0$, it maps to the same value, 4, violating the one-to-one condition where each input must map to a unique output.

Question 13

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 14

Solve the problem.
-Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Accepted Answer

To find the number of years before the use of electricity has tripled when growing at a rate of 5.8% per year compounded continuously, we use the formula for continuous compounding: $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the initial amount, $r$ is the rate of growth, and $e$ is the base of the natural logarithm. Since we want the electricity use to triple, $A/P = 3$. Substituting the values, we get $3 = e^{0.058t}$. Taking the natural logarithm of both sides gives $ln(3) = 0.058t$. Solving for $t$ gives $t = \frac{ln(3)}{0.058}$, which approximately equals 18.94 years.

Question 15

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 16

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 17

Solve the problem.
-Find the amount of interest earned on the following deposit: $1,000 at 10% compounded annually for 8 years

Accepted Answer

The answer of Solve the problem.
-Find the amount of interest...

Question 18

Solve the problem.
-Use the formu $$\mathrm { P } = \mathrm { Ie } ^ { \mathrm { kt } }$$ where P is the resulting population, I is the initial population, and t is measured in hours. A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 6 hours, what
Will it be at the end of 8 hours?

Accepted Answer

The answer of Solve the problem.
-Use the formu \[\mathrm {...

Question 19

Is the function graphed below one-to-one?
-

Accepted Answer

The answer of Is the function graphed below one-to-one?
-...

Question 20

Solve the problem.
-The amount of particulate matter left in solution during a filtering process decreases by the equation $$P = 900 ( 2 ) ^ { - 0.8 n }$$ where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

Accepted Answer

For n = 0, $P = 900(2)^{-0.8(0)} = 900(1) = 900$. For n = 5, $P = 900(2)^{-0.8(5)} \approx 900(0.0625) \approx 56$.

Quiz 2: Functions

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 9% compounded annually for 4 years

Solve the problem. -The purchasing power of a dollar is decreasing at the rate of 6.0% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.81? Round answers to the nearest hundredth.

Solve the problem. -An economist predicts that the buying power $B ( x )$ of a dollar $x$ years from now will decrease according to the formula $\mathrm { B } ( \mathrm { x } ) = 0.78 ^ { \mathrm { x } }$ . How much will today's dollar be worth in 4 years? Round the answer to the nearest cent.

Is the function graphed below one-to-one? -

Solve the problem. -The decay of 608 mg of an isotope is given by A $A ( t ) = 608 e ^ { - 0.019 t }$ , where t is time in years. Find the amount left after 50 years.

Is the function graphed below one-to-one? -

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 12% compounded annually for 7 years

Is the function graphed below one-to-one? -

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } - x - 3 , & x < 1 \\5 , & x \geq 1\end{array} \right.$

Solve the problem. -The population of a small country increases according to the functio $B = 2,400,000 e ^ { 0.05 } t$ t, where t is measured in years. How many people will the country have after 3 years?

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 , & x > 0 \\4 , & x \leq 0\end{array} \right.$

Is the function graphed below one-to-one? -

Solve the problem. -Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Is the function graphed below one-to-one? -

Is the function graphed below one-to-one? -

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 10% compounded annually for 8 years

Is the function graphed below one-to-one? -

Solve the problem. -The amount of particulate matter left in solution during a filtering process decreases by the equation $P = 900 ( 2 ) ^ { - 0.8 n }$ where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

Quiz 2: Functions

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 9% compounded annually for 4 years

Solve the problem. -The purchasing power of a dollar is decreasing at the rate of 6.0% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.81? Round answers to the nearest hundredth.

Is the function graphed below one-to-one? -

Solve the problem. -The decay of 608 mg of an isotope is given by A A(t) =608e−0.019tA ( t ) = 608 e ^ { - 0.019 t }A(t) =608e−0.019t , where t is time in years. Find the amount left after 50 years.

Is the function graphed below one-to-one? -

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 12% compounded annually for 7 years

Is the function graphed below one-to-one? -

Determine from its graph if the function is one-to-one. - f(x)={−x−3,x<15,x≥1f ( x ) = \left\{ \begin{array} { l l } - x - 3 , & x < 1 \\5 , & x \geq 1\end{array} \right.f(x)={−x−3,5,​x<1x≥1​

Solve the problem. -The population of a small country increases according to the functio B=2,400,000e0.05tB = 2,400,000 e ^ { 0.05 } tB=2,400,000e0.05t t, where t is measured in years. How many people will the country have after 3 years?

Determine from its graph if the function is one-to-one. - f(x)={x+5,x>04,x≤0f ( x ) = \left\{ \begin{array} { l l } x + 5 , & x > 0 \\4 , & x \leq 0\end{array} \right.f(x)={x+5,4,​x>0x≤0​

Is the function graphed below one-to-one? -

Solve the problem. -Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Is the function graphed below one-to-one? -

Is the function graphed below one-to-one? -

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 10% compounded annually for 8 years

Is the function graphed below one-to-one? -

Solve the problem. -The decay of 608 mg of an isotope is given by A $A ( t ) = 608 e ^ { - 0.019 t }$ , where t is time in years. Find the amount left after 50 years.

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } - x - 3 , & x < 1 \\5 , & x \geq 1\end{array} \right.$

Solve the problem. -The population of a small country increases according to the functio $B = 2,400,000 e ^ { 0.05 } t$ t, where t is measured in years. How many people will the country have after 3 years?

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 , & x > 0 \\4 , & x \leq 0\end{array} \right.$