Q: A medical researcher models the spread of a virus by $V(t) = 100e^{0.2t}$. What is the approximate value of $V(5)$? (Use $e^{1} \approx 2.718$)

$V(5) = 100e^{1} \approx 100 \times 2.718 = 271.8$

Q: A quadratic function models the height of a ball thrown upward: $h(t) = -16t^2 + 32t + 5$. What is the maximum height reached by the ball?

The maximum occurs at $t = -\frac{b}{2a} = -\frac{32}{2 \times -16} = 1$. $h(1) = -16(1)^2 + 32(1) + 5 = -16 + 32 + 5 = 21$ feet.

Q: Which of the following is the correct simplification of $\sqrt{50}$?

$\sqrt{25 \times 2} = 5\sqrt{2}$

Q: A hospital records the number of patients admitted each day as $N(d) = 12d + 5$. If 10 days have passed, how many patients have been admitted in total?

$N(10) = 12 \times 10 + 5 = 120 + 5 = 125$

Q: A scientist models the temperature of a reaction by $T(t) = 20 + 5\sin(\frac{\pi}{6}t)$, where $t$ is time in minutes. What is the temperature at $t = 6$ minutes?

$T(6) = 20 + 5\sin(\frac{\pi}{6} \times 6) = 20 + 5\sin(\pi) = 20 + 5 \times 0 = 20$

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 $a_n, \ldots, a_0$ are real numbers.

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream by $C(t) = 5t^2 - 3t + 2$, where $t$ 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 NOT a property of exponents?

Accepted Answer

$a^m + a^n = a^{m+n}$

Question 4

A biologist is studying the population growth of bacteria, modeled by $P(t) = 200 \cdot 1.5^t$. What is the population after 3 hours?

Accepted Answer

$P(3) = 200 \cdot 1.5^3 = 200 \cdot 3.375 = 675$

Question 5

Which of the following is the correct solution to the quadratic equation $x^2 - 5x + 6 = 0$?

Accepted Answer

$x = 2$ and $x = 3$

Question 6

A chemical reaction rate is modeled by $R(x) = 4x^2 - 7x + 3$. What is the rate when $x = -2$?

Accepted Answer

$R(-2) = 4(-2)^2 - 7(-2) + 3 = 16 + 14 + 3 = 33$

Question 7

Which of the following expressions is equivalent to $\frac{2x^3y^2}{4x^2y^5}$?

Accepted Answer

$\frac{x}{2y^3}$

Question 8

A student is solving the equation $2(x - 3) = 4x + 6$. What is the value of $x$?

Accepted Answer

$x = -6$

Question 9

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

Accepted Answer

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

Question 10

A medical researcher models the spread of a virus by $V(t) = 100e^{0.2t}$. What is the approximate value of $V(5)$? (Use $e^{1} \approx 2.718$)

Accepted Answer

$V(5) = 100e^{1} \approx 100 	imes 2.718 = 271.8$

Question 11

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

Accepted Answer

$x = 5, y = 2$

Question 12

A quadratic function models the height of a ball thrown upward: $h(t) = -16t^2 + 32t + 5$. What is the maximum height reached by the ball?

Accepted Answer

The maximum occurs at $t = -\frac{b}{2a} = -\frac{32}{2 	imes -16} = 1$. $h(1) = -16(1)^2 + 32(1) + 5 = -16 + 32 + 5 = 21$ feet.

Question 13

Which of the following is the correct simplification of $\sqrt{50}$?

Accepted Answer

$\sqrt{25 	imes 2} = 5\sqrt{2}$

Question 14

A company’s profit is modeled by $P(x) = -2x^2 + 8x - 6$, where $x$ is the number of units sold. How many units should be sold to maximize profit?

Accepted Answer

$x = 2$

Question 15

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

Accepted Answer

$x = 4$ or $x = -\frac{2}{3}$

Question 16

A hospital records the number of patients admitted each day as $N(d) = 12d + 5$. If 10 days have passed, how many patients have been admitted in total?

Accepted Answer

$N(10) = 12 	imes 10 + 5 = 120 + 5 = 125$

Question 17

Which of the following is the correct solution to $\frac{2x - 4}{x + 3} = 0$?

Accepted Answer

$x = 2$

Question 18

A scientist models the temperature of a reaction by $T(t) = 20 + 5\sin(\frac{\pi}{6}t)$, where $t$ is time in minutes. What is the temperature at $t = 6$ minutes?

Accepted Answer

$T(6) = 20 + 5\sin(\frac{\pi}{6} 	imes 6) = 20 + 5\sin(\pi) = 20 + 5 	imes 0 = 20$

Question 19

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

Accepted Answer

$x = -2$

College Algebra: Course Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards