Question 1

A pharmaceutical company is testing a new drug and models the concentration of the drug in the bloodstream over time with the function $C(t) = 5e^{-0.2t}$, where $t$ is in hours. What is the concentration after 8 hours?

Accepted Answer

$C(8) = 5e^{-1.6} \approx 0.92$

Question 2

Which of the following is the correct factorization of the polynomial $x^3 - 4x^2 + 4x$?

Accepted Answer

$x(x-2)^2$

Question 3

A biologist is studying population growth and models the population with the exponential function $P(t) = 2000 \cdot 1.05^t$, where $t$ is the number of years. What will the population be after 10 years?

Accepted Answer

$P(10) = 2000 \cdot 1.05^{10} \approx 3257$

Question 4

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

Accepted Answer

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

Question 5

A company’s profit $P$ (in thousands of dollars) is modeled by the function $P(x) = -2x^2 + 12x - 16$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $P(3) = 2$ thousand dollars when $x = 3$

Question 6

Which of the following functions is one-to-one?

Accepted Answer

$f(x) = 2x + 5$

Question 7

Given the rational expression $\frac{x^2 - 9}{x^2 - 6x + 9}$, which of the following is its simplified form?

Accepted Answer

$\frac{(x-3)(x+3)}{(x-3)^2}$

Question 8

A medical researcher uses the function $f(x) = \sqrt{x-1}$ to model the reaction time (in seconds) of a patient, where $x$ is the number of hours since medication was administered. What is the domain of $f(x)$?

Accepted Answer

$x \geq 1$

Question 9

Convert the logarithmic equation $\log_{2}(x) = 5$ to its equivalent exponential form.

Accepted Answer

$x = 2^5$

Question 10

Which of the following is the correct solution to the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 1$

Question 11

A car rental company charges a base fee of $\$30$ plus $\$0.20$ per mile driven. Which function models the total cost $C$ for driving $x$ miles?

Accepted Answer

$C(x) = 30 + 0.20x$

Question 12

Simplify the radical expression $\sqrt{50} + \sqrt{18}$.

Question 13

Which of the following is the inverse of the function $f(x) = 3x - 7$?

Accepted Answer

$f^{-1}(x) = \frac{x-7}{3}$

Question 14

A scientist is analyzing the decay of a radioactive substance and models the amount remaining after $t$ years as $A(t) = 100e^{-0.3t}$. After how many years will only $20$ units remain?

Accepted Answer

$t = \frac{\ln(5)}{0.3} \approx 5.36$

Question 15

Which of the following is the correct simplification of $\frac{2x^2 - 8x}{4x}$?

Accepted Answer

$\frac{x-4}{2}$

Question 16

A parabola models the path of a thrown ball: $y = -2x^2 + 8x + 3$. What is the maximum height reached by the ball?

Accepted Answer

$y = 11$ at $x = 2$

Question 17

Which of the following is the correct domain for the function $f(x) = \frac{1}{x^2 - 4}$?

Accepted Answer

$x 
eq 2$ and $x 
eq -2$

Question 18

A business uses the function $R(x) = 100x - x^2$ to model revenue, where $x$ is the number of items sold. What is the maximum revenue?

Accepted Answer

$R(50) = 2500$

Question 19

Which of the following is the correct solution to the equation $\sqrt{x+5} = 4$?

Accepted Answer

$x = 11$

College Algebra Syllabus and Study Guide Overview

Study Guide - Practice Questions

Study Guide - Flashcards