Question 1

The graphs of two functions  and  are given below. Using the graphs, determine  . 
A) 2
B) 4.8
C) 7.6
D) 15.2
E) -1.6

Accepted Answer

The answer of The graphs of two functions  and...

Question 2

Two functions and are given by the tables below. Determine . 
A) 0
B) -1
C) 5
D) 1
E) -2

Accepted Answer

The answer of Two functions and are given by the...

Question 3

A car dealer advertises a 35% discount on all cars available in the current inventory. In addition, the car dealer offers a $1800 rebate on the purchase of a new care. The dealer decides to apply the rebate first and then award the 35% discount afterwards. Let  represent the sticker price of the new car. Which one of the following functions model the final price of the car once the rebate and discount have been awarded?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A car dealer advertises a 35% discount...

Question 4

Two functions and are given by the tables below. Determine . 
A) 5
B) 3
C) 4
D) 1
E) 2

Accepted Answer

The answer of Two functions and are given by the...

Question 5

If  and  , determine  . Round to the nearest tenth.
A) 2
B) 20.1
C) -20.1
D) 7.4
E) -15.1

Accepted Answer

The answer of If  and  , determine ...

Question 6

Find the inverse of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the inverse of  .
A) 
B)...

Question 7

If  and  , determine  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If  and  , determine ...

Question 8

The mass of bacteria in a Petri dish is 56 micrograms. After 3 hours, the bacteria's mass as increased to 164 micrograms. How long will it take for the population to quadruple?
A) 1.3 hours
B) 3.9 hours
C) 0.3 hours
D) 2.9 hours
E) 1.4 hours

Accepted Answer

The answer of The mass of bacteria in a Petri...

Question 9

Find the inverse of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the inverse of  .
A) 
B)...

Question 10

Jennifer invests $5,100 in a saving certificate with an interest rate of 4.25% per year, compounded monthly. How long will it take for her investment to grow to $13,000? Round to the nearest tenth.
A) 1.9 years
B) 4.3 years
C) 215.6 years
D) 22.1 years
E) 211.5 years

Accepted Answer

To find the time it takes for an investment to grow to a certain amount with compound interest, we use the formula $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount the investment will grow to, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), $n$ is the number of times the interest is compounded per year, and $t$ is the time in years. Rearranging the formula to solve for $t$, we get $t = \frac{\log(\frac{A}{P})}{n \log(1 + \frac{r}{n})}$.Given: $A = 13,000$, $P = 5,100$, $r = 0.0425$ (4.25% as a decimal), and $n = 12$ (since the interest is compounded monthly).Plugging these values into the rearranged formula gives us the time it takes for the investment to grow to $13,000. Calculating this yields a value close to 22.1 years, making option D the correct answer.

Question 11

The half-life of Radon-222 is 3.8 days. A 32-gram sample of Radon-222 is monitored for one day. How long will it take for the sample to be 24% of the initial amount? (rounded to the nearest hundredths)?
A) 0.1 days
B) 7.8 days
C) 3.8 days
D) 1.8 days
E) 0.5 days

Accepted Answer

To find the time it takes for a sample to reduce to 24% of its initial amount, we use the half-life formula: $N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time, and $T$ is the half-life period. Here, $N_0 = 32$ grams, $N = 0.24 \times 32$ grams (since we want the sample to be 24% of the initial amount), and $T = 3.8$ days. Rearranging the formula to solve for $t$, we get $t = T \frac{\log(N/N_0)}{\log(1/2)}$. Substituting the given values, we find that $t$ is approximately 7.8 days.

Question 12

Using the graph below, determine  . 
A) 0.33
B) 0.05
C) 120
D) 19.84
E) 3

Accepted Answer

The answer of Using the graph below, determine  ....

Question 13

Find the inverse of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the inverse of  .
A) 
B)...

Question 14

The mass of bacteria in a Petri dish is 30 micrograms. After 3 hours, the bacteria s mass as increased to 141 micrograms. Which one of the following exponential functions model the bacteria s growth, where  is measured in hours.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The mass of bacteria in a Petri...

Quiz 4: Logarithmic Functions and Exponential Modela

The graphs of two functions and are given below. Using the graphs, determine .

Two functions and are given by the tables below. Determine .

Two functions and are given by the tables below. Determine .

If and , determine . Round to the nearest tenth.

Find the inverse of .

If and , determine .

The mass of bacteria in a Petri dish is 56 micrograms. After 3 hours, the bacteria's mass as increased to 164 micrograms. How long will it take for the population to quadruple?

Find the inverse of .

Jennifer invests $5,100 in a saving certificate with an interest rate of 4.25% per year, compounded monthly. How long will it take for her investment to grow to $13,000? Round to the nearest tenth.

The half-life of Radon-222 is 3.8 days. A 32-gram sample of Radon-222 is monitored for one day. How long will it take for the sample to be 24% of the initial amount? (rounded to the nearest hundredths) ?

Using the graph below, determine .

Find the inverse of .

The mass of bacteria in a Petri dish is 30 micrograms. After 3 hours, the bacteria s mass as increased to 141 micrograms. Which one of the following exponential functions model the bacteria s growth, where is measured in hours.