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 $a > 1$) 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 $a > 0$ 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 $a > 0$?

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

Study Guide - Practice Questions

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