Question 1

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

Accepted Answer

Domain: $$x \in \mathbb{R}$$, Range: $$y \u003e 0$$

Question 2

The function $$f(x) = 80e$$^{-0.3x}$$ + 20$$ models the percentage of information remembered $$x$$ weeks after learning. What percentage is remembered after 6 weeks? (Round to one decimal place.)

Accepted Answer

$$f(6) \approx 53.2$$

Question 3

Which transformation shifts the graph of $$f(x) = b^x$$ vertically upward by $$k$$ units?

Accepted Answer

$$f(x) = b^x + k$$

Question 4

Suppose you invest $$13,000$$ for 2 years. Which yields a larger amount: $$6\%$$ compounded daily or $$5.94\%$$ compounded continuously?

Accepted Answer

$$6\%$$ compounded daily

Question 5

Which of the following is the correct exponential form of $$\log_2$ 8 = 3$$?

Accepted Answer

$$2^3 = 8$

Question 6

Evaluate $$\log_{10} \sqrt{3}$$ using logarithm properties.

Accepted Answer

$$\frac{1}{2} \log_{10} 3$$

Question 7

What is the vertical asymptote of the function $$f(x) = \log_3$ (x-2)$$?

Accepted Answer

$$x = 2$$

Question 8

Expand $$\log_2$ (7 \cdot 11)$$ using logarithm properties.

Accepted Answer

$$\log_2$ 7 + \log_2$ 11$$

Question 9

Condense the expression $$2 \ln x + \frac{1}{3} \ln (x+5)$$ into a single logarithm.

Accepted Answer

$$\ln \left( x^2$ (x+5$$)^{1/3}$$ \right)$$

Question 10

Use the change-of-base property to evaluate $$\log_5$ 17 to $$four decimal places.

Accepted Answer

$$\frac{\ln 17}{\ln 5} \approx 1.5797$$

Question 11

Solve for $$x$$: $$5^x = 134. $$Round your answer to two decimal places.

Accepted Answer

$$x \approx 3.13$$

Question 12

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

Accepted Answer

$$x = 11$$

Question 13

The half-life of strontium-90 is 28 years. If there are originally 60 grams, how long will it take for strontium-90 to decay to 10 grams?

Accepted Answer

$$t \approx 74.1$$ years

Question 14

Which of the following is the correct logistic growth model for a population with carrying capacity $$c$$ and growth rate $$a$$?

Accepted Answer

$$f(t) = \frac{c}{1 + ae$$^{-kt}$$}$$

Question 15

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

Accepted Answer

Product Rule

Question 16

If $$f(x) = e^x$$ and $$g(x) = \ln x$$, which statement is true about their graphs?

Accepted Answer

The graph of $$g(x) is a $$reflection of $$f(x)$$ about the line $$y = x$$

Question 17

Which of the following is the correct domain of $$h(x) = \ln(3-x)$$?

Accepted Answer

$$x \u003c 3$$

Question 18

Given the exponential growth model $$A = A_0$ e$$^{kt}$$, which of the following statements is true if k$$ \u003c 0$$?

Accepted Answer

The function models exponential decay.

Question 19

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

Accepted Answer

$$x = -0.5$$

Exponential and Logarithmic Functions: Definitions, Properties, Graphs, and Applications

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