Q: A loan of $\$5,000$ is taken out at an annual interest rate of 6%, compounded quarterly. What is the value of the loan after 2 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

$5,000 \times (1 + \frac{0.06}{4})^{8}$

Question 1

Which of the following best describes the domain of the function $f(x) = \dfrac{1}{x-3}$?

Accepted Answer

All real numbers except $x = 3$

Question 2

A company models its profit $P$ (in thousands of dollars) as a function of the number of units sold $x$ by $P(x) = -2x^2 + 40x - 100$. What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $300$ at $x = 10$

Question 3

Which of the following equations represents an exponential decay function?

Accepted Answer

$f(x) = 5 \cdot 0.8^x$

Question 4

Given the function $f(x) = 2x + 5$ and $g(x) = x^2$, what is $(f \circ g)(3)$?

Accepted Answer

$2 \cdot 9 + 5 = 23$

Question 5

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $P$ after $t$ hours?

Accepted Answer

$P(t) = 200 \cdot 3^{t/4}$

Question 6

Which of the following is the inverse of the function $f(x) = 4x - 7$?

Accepted Answer

$f^{-1}(x) = \dfrac{x - 7}{4}$

Question 7

A car depreciates in value by 15% each year. If the car is currently worth $\$20,000$, what will its value be after 3 years?

Accepted Answer

$20,000 	imes (0.85)^3$

Question 8

Which of the following graphs represents a function?

Accepted Answer

A graph where every vertical line crosses the curve at most once

Question 9

Solve for $x$: $2^{x+1} = 32$

Accepted Answer

$x = 4$

Question 10

A loan of $\$5,000$ is taken out at an annual interest rate of 6%, compounded quarterly. What is the value of the loan after 2 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

Accepted Answer

$5,000 	imes (1 + \frac{0.06}{4})^{8}$

Question 11

Which of the following is the solution set for the equation $|2x - 5| = 9$?

Accepted Answer

$x = 7$ or $x = -2$

Question 12

If $f(x) = x^2 - 4x + 3$, what are the $x$-intercepts of the function?

Accepted Answer

$x = 1$ and $x = 3$

Question 13

Which of the following best describes the range of the function $f(x) = \sqrt{x - 2}$?

Accepted Answer

All real numbers $y \geq 0$

Question 14

A radioactive substance decays according to the formula $A(t) = A_0 e^{-kt}$. If $A_0 = 100$ grams and $k = 0.05$, how much remains after 10 years?

Accepted Answer

$100 e^{-0.5}$ grams

Question 15

Which of the following is a solution to the equation $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 16

A geometric sequence has first term $a_1 = 6$ and common ratio $r = 2$. What is the 5th term?

Accepted Answer

$a_5 = 96$

Question 17

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

Accepted Answer

It is an even function

Question 18

A real-world application: The height $h$ (in meters) of a ball thrown upward from the ground with an initial velocity of $20$ m/s is given by $h(t) = 20t - 4.9t^2$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$t = 2.04$ seconds

Question 19

Which of the following is the solution to the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 3$

College Algebra (MATH-120) Syllabus and Study Guide

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