$$C_{exp} = 1000 \times C_{std}$$

Question 1

Which of the following functions is one-to-one and therefore invertible?

Accepted Answer

$$f(x) = 2x + 3$$

Question 2

Given $$f(x) = 3x - 7$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{3}$$

Question 3

If $$f(x) = \sqrt{x - 2}$$ for $$x \geq 2$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$x \geq 0$$

Question 4

Which property of exponents is illustrated by $$a^{m}$$ \cdot $$a^{n}$$ = $$a^{m+n}$$?

Accepted Answer

Product of powers with the same base

Question 5

Solve for $$x$$: $$2^{x} = 36$

Accepted Answer

$$x = \log$$_{2}$$36$$

Question 6

Which of the following is the correct logarithmic form of $$3^{4} = 81$?

Accepted Answer

$$\log$$_{3}$$81 = 4$$

Question 7

If $$pH = -\log[H$$^{+}$$]$$ and a solution has $$[H$$^{+}$$] = 6.3 	imes 10$$^{-4}$$, what is its pH?

Accepted Answer

$$pH = 4.8$$

Question 8

Given $$A(t) = 500e$$^{-0.032t}$$ models the decay of lead-210, what is the half-life of lead-210?

Accepted Answer

$$t = \frac{\ln 2}{0.032}$$

Question 9

If $$f(x) = e$$^{x-5}$$, what is f$$^{-1}$$(x)$$?

Accepted Answer

Question 10

A bank offers 4% annual interest compounded continuously. If $$5000 is $$invested, how much will be in the account after 8 years?

Accepted Answer

$$5000e^{0.32}$$

Question 11

Which of the following is the correct change-of-base formula for $$\log$$_{a}$$b$$?

Accepted Answer

$$\log$$_{a}$$b = \frac{\log$$_{10}$$b}{\log$$_{10}$$a}$$

Question 12

If the doubling time for a population is 5 years, what is the annual growth rate $$r in $$the exponential model $$P(t) = P$$_{0}$$e^{rt}$?

Accepted Answer

$$r = \frac{\ln 2}{5}$$

Question 13

Suppose $$f(x) is $$the number of cars that can be built for $$x$$ dollars. What does $$f^{-1}(1000$$)$$ represent?

Accepted Answer

The cost to build 1000 cars

Question 14

If $$f(x) = \log_{2}(x-1)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e 1$$

Question 15

Which of the following is equivalent to $$\log_{2}(8x)$$?

Accepted Answer

$$3 + \log$$_{2}$$x$$

Question 16

A radioactive substance has 12 g present initially and 6 g after 4 years. How much will remain after 7 years?

Accepted Answer

$$3.375 g$$

Question 17

If $$f(x) = 2$$^{x}$$ and g(x$$) = $$6^{x-1}$$, which function grows faster as $$x$$ increases?

Accepted Answer

$$g(x)$$

Question 18

If $$y = \log_{10}\left(\frac{C_{exp}}{C_{std}}\right)$$ and $$y = 3$$, what is the experimental concentration $$C_{exp} in $$terms of $$C_{std}$$?

Accepted Answer

$$C_{exp} = 1000 	imes C_{std}$$

Question 19

If $$f(x) = 2x + 4$$ and $$g(x) = \frac{x}{2} - 2$$, are $$f$$ and $$g$$ inverses of each other?

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Precalculus Study Guide: Exponential and Logarithmic Functions, Inverses, and Applications

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