Question 1

Which of the following best describes the domain and range of the exponential function $$f(x) = b^x$$ where $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

Domain: $$\{x : -\infty  0\}$$

Question 2

If $$f(x) = 2^x$$, which of the following statements is true about $$f(x)$$?

Accepted Answer

$$f(x) is an $$increasing function for all $$x$$

Question 3

Given the exponent rule $$b^x \cdot b^y = b$$^{x+y}$$, what is the value of 3^4$ \cdot 3^2$?

Accepted Answer

$$3^6$$

Question 4

A biologist models the growth of a bacteria population with $$P(t) = 5^t. $$What is the population after 3 hours?

Accepted Answer

$$125$$

Question 5

Which of the following is the correct interpretation of $$b^{-x}$$ for $$b \u003e 0$$?

Accepted Answer

$$b^{-x}$$ = \dfrac{1}{b^x}$$

Question 6

If $$f(x) = b^x$$ and $$b \u003e 1$$, which of the following statements is true?

Accepted Answer

$$f(x)$$ increases as $$x$$ increases

Question 7

A patient’s medication concentration is modeled by $$C(t) = 0.5^t$$ where $$t is in $$hours. What is the concentration after 4 hours?

Accepted Answer

$$0.0625$$

Question 8

Which exponent rule allows you to simplify $$(b^x)^y$$?

Accepted Answer

$$(b^x)^y = b$$^{xy}$$

Question 9

If $$f(x) = 10^x$$, what is $$f(-2)$$?

Accepted Answer

$$0.01$$

Question 10

Which of the following is the inverse function of $$f(x) = b^x$$ for $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

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

Question 11

A radioactive substance decays according to $$A(t) = 8 \cdot (0.5)^t. $$How much remains after 3 hours?

Accepted Answer

$$1$$

Question 12

Which of the following is true for all exponential functions $$f(x) = b^x$$ with $$b \u003e 0$$?

Accepted Answer

$$f(0) = 1$$

Question 13

If $$b = 16$$ and $$x = \dfrac{3}{4}$$, what is $$16^{3/4}$$?

Accepted Answer

$$8$$

Question 14

Which of the following best explains why $$b^x is $$always positive for any real $$x$$ and $$b \u003e 0$$?

Accepted Answer

Because the exponential function never crosses the $$x-$$axis

Question 15

A population doubles every hour. If the initial population is $$P_0$$, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2^t$$

Question 16

If $$b \u003e 1$$, which of the following statements about the graph of $$f(x) = b^x is $$correct?

Accepted Answer

The graph passes through $$(0, 1)$$ and increases as $$x$$ increases

Question 17

Which of the following is a correct application of the exponent rule $$\dfrac{b^x}{b^y} = b$$^{x-y}$$?

Accepted Answer

$$\dfrac{5^7$}{5^3$} = 5$$^{4}$$

Question 18

A savings account grows according to $$A(t) = 1000 \cdot 1.05^t$$, where $$t is $$the number of years. What is the account balance after 2 years?

Accepted Answer

$$1102.5$$

Question 19

If $$b^x is $$defined for all real $$x$$, which of the following is true about its domain?

Accepted Answer

The domain is $$\{x : -\infty \u003c x \u003c \infty\}$$

Question 20

Which of the following is the correct simplification of $$2^{3}$$ \cdot $$2^{-5}$$?

Accepted Answer

$$2^{-2}$$

Exponential Functions and Their Properties

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