Q: A car's value depreciates by 15% each year. If the car is currently worth $\$20,000$, what will its value be after 3 years? (Round to the nearest dollar.)

$V = 20000 \times (0.85)^3 \approx \$12,281$

Q: A chemical reaction follows the equation $A = A_0 e^{-kt}$, where $A_0$ is the initial amount and $k$ is a positive constant. If $A_0 = 100$ grams, $k = 0.2$, how much remains after 5 hours? (Round to the nearest gram.)

$A = 100e^{-1} \approx 37$ grams

Q: A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = -2x^2 + 12x + 20$, where $x$ is the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Maximum revenue is $R(3) = 38$ at $x = 3$ thousand units

Q: A student invests $\$1,000$ in an account that pays 6% annual interest compounded quarterly. What will the balance be after 2 years? (Round to the nearest dollar.)

$A = 1000 \left(1 + \dfrac{0.06}{4}\right)^{8} \approx \$1,127$

Question 1

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

Accepted Answer

$(-\infty, 3) \cup (3, \infty)$

Question 2

A pharmaceutical company models the concentration $C$ (in mg/L) of a drug in the bloodstream $t$ hours after injection by $C(t) = 5e^{-0.4t}$. What is the concentration after 3 hours? (Round to two decimal places.)

Accepted Answer

$C(3) = 5e^{-1.2} \approx 1.51$ mg/L

Question 3

Which of the following is the solution set for the equation $2x^2 - 8x + 6 = 0$?

Accepted Answer

$x = 2 \pm \sqrt{2}$

Question 4

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

Accepted Answer

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

Question 5

Which of the following is the inverse of the function $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \dfrac{x-5}{2}$

Question 6

A quadratic function models the height $h$ (in meters) of a ball thrown upward from a building: $h(t) = -4.9t^2 + 19.6t + 50$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$t = 2$ seconds

Question 7

Solve the system of equations: $\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$

Accepted Answer

$x = 2,\ y = 1$

Question 8

Which of the following is the correct factorization of $x^2 - 9x + 20$?

Accepted Answer

$(x-4)(x-5)$

Question 9

A car's value depreciates by 15% each year. If the car is currently worth $\$20,000$, what will its value be after 3 years? (Round to the nearest dollar.)

Accepted Answer

$V = 20000 	imes (0.85)^3 \approx \$12,281$

Question 10

Which of the following is the solution to the inequality $3x - 7 < 2x + 5$?

Accepted Answer

$x < 12$

Question 11

A chemical reaction follows the equation $A = A_0 e^{-kt}$, where $A_0$ is the initial amount and $k$ is a positive constant. If $A_0 = 100$ grams, $k = 0.2$, how much remains after 5 hours? (Round to the nearest gram.)

Accepted Answer

$A = 100e^{-1} \approx 37$ grams

Question 12

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

Accepted Answer

$x = 32$

Question 13

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = -2x^2 + 12x + 20$, where $x$ is the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $R(3) = 38$ at $x = 3$ thousand units

Question 14

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

Accepted Answer

$x = 7,\ x = -2$

Question 15

A student invests $\$1,000$ in an account that pays 6% annual interest compounded quarterly. What will the balance be after 2 years? (Round to the nearest dollar.)

Accepted Answer

$A = 1000 \left(1 + \dfrac{0.06}{4}\right)^{8} \approx \$1,127$

Question 16

Which of the following is the solution to the equation $x^2 + 4x + 8 = 0$?

Accepted Answer

$x = -2 \pm 2i$

Question 17

A rectangle has a length that is 3 meters more than twice its width. If the area is $33$ square meters, what is the width?

Accepted Answer

$3$ meters

Question 18

Which of the following is the solution to the system of equations $\begin{cases} x + y = 8 \ x - y = 2 \end{cases}$?

Accepted Answer

$x = 5,\ y = 3$

Question 19

If $f(x) = x^2 - 4x + 7$, what is the minimum value of $f(x)$?

Accepted Answer

$3$

Question 20

A cell phone plan charges a base fee of $\$25$ per month plus $\$0.10$ per text message. Which equation models the monthly cost $C$ for $n$ text messages?

Accepted Answer

$C = 25 + 0.10n$

College Algebra (MATH-1314) Course Overview and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards