Q: Which of the following is the correct definition of an exponential function?

$$f(x) = a^x$$, where $$a \u003e 0$$ and $$a \neq 1$$

Question 1

Which of the following best describes the inverse of a function $$f$$?

Accepted Answer

The function that interchanges the first and second coordinates of each ordered pair in $$f.$$

Question 2

Given the relation $$g = \{(1,4), (-1,9), (1,-4), (0,0)\}$$, what is the inverse of $$g$$?

Accepted Answer

$$\{(4,1), (9,-1), (-4,1), (0,0)\}$$

Question 3

Which test determines if a function is one-to-one by checking if any horizontal line intersects the graph more than once?

Accepted Answer

Horizontal-Line Test

Question 4

Which of the following is the correct formula for compound interest compounded $$k$$ times per year?

Accepted Answer

$$A = P \left(1 + \frac{r}{k}\$$right)^{kt}$$

Question 5

If $$P = 1000$$, $$r = 0.09$$, $$k = 4$$, and $$t = 5$$, what is the value of $$A$$ using the compound interest formula? (Round to two decimal places)

Accepted Answer

$$A \approx 1553.08$$

Question 6

Which of the following is the correct definition of an exponential function?

Accepted Answer

$$f(x) = a^x$$, where $$a \u003e 0$$ and $$a 
eq 1$$

Question 7

Simplify $$\log_{10} 10^5$.

Accepted Answer

$$5$$

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

Express $$\log_b \left(\frac{M}{N}\right) in $$terms of $$\log_b M$$ and $$\log_b N.$$

Accepted Answer

$$\log_b M - \log_b N$$

Question 10

If $$\log_2$ 2 = 0.301$$ and $$\log_3$ 3 = 0.477$$, what is $$\log_6$ 6$$?

Accepted Answer

$$0.778$$

Question 11

Which of the following is the correct exponential form of $$\log_3$ x = 4$$?

Accepted Answer

$$x = 3^4$

Question 12

If the population of a city grows according to $$P(t) = P_0$ e$$^{rt}$$, and P_0$ = 100,000$$, $$r = 0.02$$, how long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.02}$$

Question 13

Which of the following is the correct formula for continuously compounded interest?

Accepted Answer

$$A = Pe$$^{rt}$$

Question 14

If $$A = 2000$$, $$P = 1000$$, $$r = 0.07$$, and interest is compounded continuously, how long will it take for the investment to double?

Accepted Answer

$$t = \frac{\ln 2}{0.07}$$

Question 15

Which of the following is the correct logarithmic form of $$2^x = 8$$?

Accepted Answer

$$x = \log_2$ 8$$

Question 16

Simplify $$\log_5$ 25.$$

Accepted Answer

$$2$$

Question 17

If $$f(x) = 2x + 3$$, what is the equation of the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-3}{2}$$

Question 18

Which of the following is true about the function $$f(x) = x^2$?

Accepted Answer

It is not one-to-one because it fails the horizontal-line test.

Question 19

If $$\log_b x = y$$, which of the following is the equivalent exponential form?

Accepted Answer

$$x = b^y$$

Question 20

A scientist is studying bacteria growth modeled by $$N(t) = 500 e$$^{0.04t}$$. How many bacteria will there be after 10$ hours? (Round to the nearest whole number)

Accepted Answer

$$N(10) \approx 746$$

College Algebra Study Guide: Inverse, Exponential, Logarithmic Functions, and Applications

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