Question 1

Which of the following is the correct definition of an exponential function with base $$a$$?

Accepted Answer

$$f(x) = a^x$$

Question 2

Given the exponential function $$f(x) = 4^x$$, what is the value of $$f(3)$$?

Accepted Answer

$$64$$

Question 3

Which of the following statements about the graph of $$f(x) = a^x ($$where $$a \u003e 1) is $$TRUE?

Accepted Answer

The $$x-$$axis ($$y=0) is a $$horizontal asymptote

Question 4

Evaluate $$f(-2)$$ for the function $$f(x) = 5^x.$$

Accepted Answer

$$1/25$$

Question 5

If $$f(x) = \left(\frac{1}{2}\right)^x$$, what is $$f(-3)$$?

Accepted Answer

$$8$$

Question 6

Which of the following is the correct application of the zero exponent rule?

Accepted Answer

$$a^0 = 1$

Question 7

Solve for $$x$$: $$6^{5x-7} = 216$

Accepted Answer

$$x = 2$$

Question 8

Which of the following is the correct property for solving $$a^u = a^v$$?

Accepted Answer

$$u = v$$

Question 9

What is the domain and range of the exponential function $$f(x) = a^x$$ for $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 10

If $$f(x) = e^x$$, where $$e \approx 2.71828$$, which of the following is TRUE?

Accepted Answer

$$e is a $$real number and not a variable

Question 11

Solve for $$x$$: $$e^{4x-1}$$ = $$e^{-7x}$$

Accepted Answer

$$x = 1/11$$

Question 12

Which of the following is the correct application of the negative exponent rule?

Accepted Answer

$$a^{-n} = 1/a^n$

Question 13

A biologist models the growth of a bacteria population with $$P(t) = 3^t. If $$the initial population is 1, what will the population be after 4 hours?

Accepted Answer

$$81$$

Question 14

Which of the following is the correct application of the power of a product rule?

Accepted Answer

$$(ab)^n = a^n b^n$$

Question 15

Solve for $$x$$: $$2^{x+1}$$ = $$3^{x-1}$$

Accepted Answer

$$x = 26$$

Question 16

Which of the following is the correct application of the quotient rule for exponents?

Accepted Answer

$$\frac{a^m}{a^n} = a$$^{m-n}$$

Question 17

Solve for $$x$$: $$\left(\frac{2}{3}\right)^x = \frac{125}{8}$$

Accepted Answer

$$x = -3$$

Question 18

Which of the following points is always on the graph of $$f(x) = a^x$$ for any $$a \u003e 0$$?

Accepted Answer

$$(1, a)$$

Question 19

A medication's concentration in the bloodstream decreases according to $$C(t) = 0.5^t$$, where $$t is in $$hours. What is the concentration after 3 hours if the initial concentration is 1 unit?

Accepted Answer

$$0.125$$

Exponential Functions and Their Properties: College Algebra Study Notes

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