Question 1

Which of the following best describes the general form of an exponential function?

Accepted Answer

$$f(x) = a \cdot b^x$$

Question 2

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/3}$$

Question 3

Which property of logarithms allows you to rewrite $$\ln(ab) as$$ $$\ln(a) + \ln(b)$$?

Accepted Answer

Product Property

Question 4

Solve for $$x$$: $$2^x = 20$$

Accepted Answer

$$x = \log_2${20}$$

Question 5

Which of the following is equivalent to $$\log_b{a^n}$$?

Accepted Answer

$$n \cdot \log_b{a}$$

Question 6

The half-life of a radioactive substance is 10 years. If you start with 80 grams, how much remains after 30 years?

Accepted Answer

$$10$$ grams

Question 7

Which equation represents the inverse of the exponential function $$f(x) = 3^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_3$${x}$$

Question 8

If $$\log_5${x} = 3$$, what is the value of $$x$$?

Accepted Answer

$$125$$

Question 9

Which of the following is the correct solution to $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln{7}$$

Question 10

A car depreciates in value by 12% each year. If its initial value is $$V_0$$, which equation models its value $$V$$ after $$t$$ years?

Accepted Answer

$$V = V_0$ \cdot (0.88)^t$$

Question 11

Which of the following is the correct application of the change of base formula for $$\log_2${15}$$?

Accepted Answer

$$\frac{\ln{15}}{\ln{2}}$$

Question 12

Which of the following best describes the graph of $$y = \log_b{x}$$ for $$b \u003e 1$$?

Accepted Answer

It increases slowly for large $$x$$ and passes through $$(1, 0)$$

Question 13

If $$f(x) = 2^x$$ and $$g(x) = \log_2${x}$$, which statement is true?

Accepted Answer

$$g(f(x)) = x$$

Question 14

Which equation models continuous compound interest, where $$A is $$the amount after $$t$$ years, $$P is $$the principal, $$r is $$the annual rate, and $$t is $$time?

Accepted Answer

$$A = P e$$^{rt}$$

Question 15

Which of the following is the correct solution to $$\log_4${(x-1)} = 2$$?

Accepted Answer

$$x = 17$$

Question 16

A medication's concentration in the bloodstream decreases exponentially according to $$C(t) = 50e$$^{-0.3t}$$, where t$ is in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 50e$$^{-1.5}$$ \approx 11.16$$

Question 17

Which of the following is a solution to the equation $$\ln{x} = 0$$?

Accepted Answer

$$x = 1$$

Question 18

If $$f(x) = e^x$$ and $$g(x) = \ln{x}$$, what is $$f(g(7))$$?

Accepted Answer

$$7$$

Question 19

Which of the following is the correct domain of the function $$f(x) = \log_3${(x-2)}$$?

Accepted Answer

$$x \u003e 2$$

Question 20

A scientist models the growth of a cell culture with $$N(t) = 1000e$$^{0.05t}$$, where t$ is in hours. How long will it take for the culture to reach 2000 cells?

Accepted Answer

$$t = \frac{\ln{2}}{0.05} \approx 13.86$$ hours

Exponential and Logarithmic Functions: AP Precalculus Unit 2 Study Guide

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