Question 1

Which of the following best describes the domain and range of the exponential function $$f(x) = 3^x$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 2

The function $$f(x) = 42.2(1.56)^x$$ models the average amount spent, $$f(x)$$, in dollars, at a shopping mall after $$x$$ hours. What is the average amount spent after 3 hours, rounded to the nearest dollar?

Accepted Answer

$$162$$

Question 3

Which of the following statements is TRUE about the graph of $$f(x) = b^x$$ for $$0 \u003c b \u003c 1$$?

Accepted Answer

The graph decreases as $$x$$ increases.

Question 4

If $$f(x) = e^x$$, which of the following is the $$y-$$intercept of its graph?

Accepted Answer

$$(0, 1)$$

Question 5

A $$25,000$$ investment is made at $$7\%$$ annual interest, compounded continuously for $$5$$ years. What is the accumulated value, rounded to the nearest cent? (Use $$A = Pe$$^{rt}$$)

Accepted Answer

$$35,263.50$$

Question 6

Which of the following is the correct equivalent exponential form of $$2 = \log_b 25$$?

Accepted Answer

$$b^2 = 25$

Question 7

Evaluate $$\log_5$ 125.$$

Accepted Answer

$$3$$

Question 8

Which property of logarithms allows you to write $$\log_b(MN) = \log_b M + \log_b N$$?

Accepted Answer

Product Rule

Question 9

What is the domain of the function $$f(x) = \ln(x-2)$$?

Accepted Answer

$$(2, \infty)$$

Question 10

Which of the following is the correct condensed form of $$\ln x + 2\ln y - \ln z$$?

Accepted Answer

$$\ln\left(\dfrac{xy^2$}{z}\right)$$

Question 11

Solve for $$x$$: $$5^{3x-6} = 125$.

Accepted Answer

$$x = 3$$

Question 12

Which of the following is the correct solution to $$\log_2$(x-4) = 3$$?

Accepted Answer

$$x = 12$$

Question 13

A radioactive substance has a half-life of 28 years. If there are originally 60 grams, how long will it take to decay to 10 grams? (Use $$A = A_0$ e$$^{kt}$$, k$$ = \frac{\ln(1/2)}{28}$$)

Accepted Answer

$$46.6$$ years

Question 14

Which of the following is the correct inverse of the function $$f(x) = e^x$$?

Accepted Answer

$$f^{-1}(x$$) = \ln x$$

Question 15

The function $$f(x) = 78 - 15 \ln(t+1)$$ models the average score $$f(t)$$ after $$t$$ months. What was the average score on the original exam?

Accepted Answer

$$78$$

Question 16

Which of the following is the correct change-of-base formula for $$\log_2$ 7$$?

Accepted Answer

$$\dfrac{\log 7}{\log 2}$$

Question 17

A population grows from 807 million to 1052 million in 11 years. Using the exponential growth model $$A = A_0$ e$$^{kt}$$, what is the value of k$ (rounded to four decimal places)?

Accepted Answer

$$k = 0.0240$$

Question 18

Which of the following transformations shifts the graph of $$f(x) = \log_2$ x to $$the right by 3 units?

Accepted Answer

$$g(x) = \log_2$(x-3)$$

Question 19

Which of the following is the correct solution to $$e^{x+4}$$ = \dfrac{1}{$$e^{2x}$$}$$?

Accepted Answer

$$x = -2$$

Question 20

The function $$f(x) = 80e$$^{-0.3x}$$ + 20$$ describes the percentage of information remembered $$x$$ weeks after learning. What percentage is remembered after 8 weeks? (Round to one decimal place.)

Accepted Answer

$$34.8\%$$

Exponential and Logarithmic Functions: Properties, Graphs, and Transformations

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