Q: A biologist models the population of a bacteria culture with $P(t) = 500e^{0.3t}$, where $t$ is time in hours. What is the population after 5 hours?

$P(5) = 500e^{0.3 \times 5} = 500e^{1.5} \approx 500 \times 4.4817 \approx 2240.85$

Q: A company’s profit $P$ (in dollars) is modeled by $P(x) = -2x^2 + 120x - 1000$, where $x$ is the number of units sold. How many units must be sold to maximize profit?

$x = \dfrac{-b}{2a} = \dfrac{-120}{2 \times -2} = \dfrac{-120}{-4} = 30$

Q: A medical researcher uses the exponential decay model $N(t) = 1000e^{-0.2t}$ to describe the amount of a drug in the bloodstream after $t$ hours. How much drug remains after 8 hours?

$N(8) = 1000e^{-0.2 \times 8} = 1000e^{-1.6} \approx 1000 \times 0.2019 \approx 201.9$

Q: A car’s value $V$ depreciates according to $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value after 3 years?

$V(3) = 20000(0.85)^3 = 20000 \times 0.614125 = 12282.50$

Q: A student invests $\$500$ in an account that earns $6\%$ annual interest compounded monthly. What is the value after 2 years? Use $A = P\left(1 + \dfrac{r}{n}\right)^{nt}$.

$A = 500\left(1 + \dfrac{0.06}{12}\right)^{24} \approx 500 \times 1.1275 = 563.75$

Q: A chemical reaction is modeled by $C(t) = 100(1 - e^{-0.4t})$, where $C$ is the concentration after $t$ minutes. What is the concentration after 10 minutes?

$C(10) = 100(1 - e^{-0.4 \times 10}) = 100(1 - e^{-4}) \approx 100(1 - 0.0183) = 98.17$

Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation in which each input is paired with exactly one output.

Question 2

Given the function $f(x) = 2x^2 - 3x + 5$, what is $f(-2)$?

Accepted Answer

$f(-2) = 2(-2)^2 - 3(-2) + 5 = 8 + 6 + 5 = 19$

Question 3

Which of the following equations represents a linear function?

Accepted Answer

$y = 4x - 7$

Question 4

A biologist models the population of a bacteria culture with $P(t) = 500e^{0.3t}$, where $t$ is time in hours. What is the population after 5 hours?

Accepted Answer

$P(5) = 500e^{0.3 	imes 5} = 500e^{1.5} \approx 500 	imes 4.4817 \approx 2240.85$

Question 5

Which of the following is the solution set for the inequality $2x - 5 > 9$?

Accepted Answer

$x > 7$

Question 6

A company’s profit $P$ (in dollars) is modeled by $P(x) = -2x^2 + 120x - 1000$, where $x$ is the number of units sold. How many units must be sold to maximize profit?

Accepted Answer

$x = \dfrac{-b}{2a} = \dfrac{-120}{2 	imes -2} = \dfrac{-120}{-4} = 30$

Question 7

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

Accepted Answer

$(x, y) = (2, 3)$

Question 8

Which of the following is the domain of the function $f(x) = \dfrac{1}{x-4}$?

Accepted Answer

$x \in \mathbb{R}, x 
eq 4$

Question 9

A medical researcher uses the exponential decay model $N(t) = 1000e^{-0.2t}$ to describe the amount of a drug in the bloodstream after $t$ hours. How much drug remains after 8 hours?

Accepted Answer

$N(8) = 1000e^{-0.2 	imes 8} = 1000e^{-1.6} \approx 1000 	imes 0.2019 \approx 201.9$

Question 10

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

Accepted Answer

$(x - 3)(x + 3)$

Question 11

A car’s value $V$ depreciates according to $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value after 3 years?

Accepted Answer

$V(3) = 20000(0.85)^3 = 20000 	imes 0.614125 = 12282.50$

Question 12

Which of the following is the solution to $|3x - 7| = 5$?

Accepted Answer

$x = 4$ or $x = \dfrac{2}{3}$

Question 13

Which of the following is the correct solution to the quadratic equation $x^2 - 6x + 8 = 0$?

Accepted Answer

$x = 2$ or $x = 4$

Question 14

A student invests $\$500$ in an account that earns $6\%$ annual interest compounded monthly. What is the value after 2 years? Use $A = P\left(1 + \dfrac{r}{n}\right)^{nt}$.

Accepted Answer

$A = 500\left(1 + \dfrac{0.06}{12}ight)^{24} \approx 500 	imes 1.1275 = 563.75$

Question 15

Which of the following is the inverse function of $f(x) = 3x + 2$?

Accepted Answer

$f^{-1}(x) = \dfrac{x - 2}{3}$

Question 16

Which of the following is the correct solution to the equation $\log_{2}(x) = 5$?

Accepted Answer

$x = 32$

Question 17

A chemical reaction is modeled by $C(t) = 100(1 - e^{-0.4t})$, where $C$ is the concentration after $t$ minutes. What is the concentration after 10 minutes?

Accepted Answer

$C(10) = 100(1 - e^{-0.4 	imes 10}) = 100(1 - e^{-4}) \approx 100(1 - 0.0183) = 98.17$

Question 18

Which of the following is the correct solution to the equation $2^{x} = 20$?

Accepted Answer

$x = \log_{2}(20) \approx 4.32$

Question 19

Which of the following is the range of the function $f(x) = x^2 - 4$?

Accepted Answer

$y \geq -4$

College Algebra Syllabus and Course Overview

Study Guide - Practice Questions

Study Guide - Flashcards