Q: A hospital uses the formula $P = 1200e^{0.03t}$ to model the number of bacteria present after $t$ hours. What is the approximate number of bacteria after 10 hours? (Round to the nearest whole number)

$P = 1200e^{0.3} \approx 1200 \times 1.3499 \approx 1620$

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

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

Q: A biologist models the growth of a plant with $h(t) = 2t^2 + 5t + 3$, where $h$ is the height in cm and $t$ is time in weeks. What is the height after 6 weeks?

$h(6) = 2(6)^2 + 5(6) + 3 = 72 + 30 + 3 = 105$ cm

Question 1

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

Accepted Answer

A function that can be written as $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, where $n$ is a non-negative integer and $a_n 
eq 0$.

Question 2

A chemical reaction is modeled by the equation $C(t) = 5t^2 - 3t + 2$, where $C$ is the concentration in mol/L and $t$ is time in hours. What is the concentration after 4 hours?

Accepted Answer

$C(4) = 5(4)^2 - 3(4) + 2 = 80 - 12 + 2 = 70$

Question 3

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

Accepted Answer

$x = 7$ and $x = -2$

Question 4

A hospital uses the formula $P = 1200e^{0.03t}$ to model the number of bacteria present after $t$ hours. What is the approximate number of bacteria after 10 hours? (Round to the nearest whole number)

Accepted Answer

$P = 1200e^{0.3} \approx 1200 	imes 1.3499 \approx 1620$

Question 5

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 6

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

Accepted Answer

Maximum profit is $P(3) = -2(3)^2 + 12(3) - 16 = -18 + 36 - 16 = 2$ thousand dollars, at $x = 3$ thousand units.

Question 7

Which of the following is the correct domain of the function $f(x) = \frac{1}{x^2 - 9}$?

Accepted Answer

All real numbers except $x = 3$ and $x = -3$

Question 8

Solve the inequality $3x - 7 < 2x + 5$.

Accepted Answer

$x < 12$

Question 9

A population of bacteria doubles every 5 hours. If the initial population is 500, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 500 	imes 2^{t/5}$

Question 10

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

Accepted Answer

$x = 32$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$x = 2$ and $x = 4$

Question 13

A student is analyzing the function $f(x) = \sqrt{x - 3}$. What is the domain of $f(x)$?

Accepted Answer

$x \geq 3$

Question 14

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

Accepted Answer

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

Question 15

A biologist models the growth of a plant with $h(t) = 2t^2 + 5t + 3$, where $h$ is the height in cm and $t$ is time in weeks. What is the height after 6 weeks?

Accepted Answer

$h(6) = 2(6)^2 + 5(6) + 3 = 72 + 30 + 3 = 105$ cm

Question 16

Which of the following is the correct solution to the equation $2^{x} = 64$?

Accepted Answer

$x = 6$

Question 17

A student is asked to solve the rational equation $\frac{x}{x-2} = 3$. What is the solution?

Accepted Answer

$x = 6$

Question 18

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

Accepted Answer

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

Question 19

A student is analyzing the graph of $y = -x^2 + 4x - 3$. What is the vertex of the parabola?

Accepted Answer

$(2, 1)$

College Algebra Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards