Q: A radioactive substance decays according to $A(t) = 200e^{-0.1t}$, where $t$ is in years. How long will it take for the substance to decay to half its original amount?

$t = \frac{\ln(0.5)}{-0.1} \approx 6.93$ years

Q: A rectangle has a length that is 3 units more than twice its width. If the perimeter is 36 units, what are the rectangle’s dimensions?

Width = 5 units, Length = 13 units

Question 1

Which of the following is the correct definition of the domain of a function $f(x)$?

Accepted Answer

The set of all $x$ values for which $f(x)$ is defined.

Question 2

A hospital records the number of patients admitted each day as a function $P(d)$, where $d$ is the day of the month. If $P(15) = 42$, what does this value represent?

Accepted Answer

42 patients were admitted on the 15th day of the month.

Question 3

Which of the following equations represents a linear function?

Accepted Answer

$f(x) = 2x + 5$

Question 4

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

Accepted Answer

$C = 30 + 0.20m$

Question 5

Given the quadratic function $f(x) = x^2 - 6x + 8$, what are its zeros?

Accepted Answer

$x = 2$ and $x = 4$

Question 6

A biologist models the population of a species with the exponential function $P(t) = 500e^{0.03t}$, where $t$ is time in years. What is the population after 10 years?

Accepted Answer

$P(10) = 500e^{0.3} \approx 674$

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

$x = 3, y = 1$

Question 8

A medication’s concentration in the bloodstream decreases exponentially according to $C(t) = 100e^{-0.5t}$, where $t$ is in hours. What is the concentration after 4 hours?

Accepted Answer

$C(4) = 100e^{-2} \approx 13.53$

Question 9

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

Accepted Answer

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

Question 10

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 $P(3) = 2$ thousand dollars, at $x = 3$ thousand units.

Question 11

Which of the following is the solution set for $|2x - 5| = 7$?

Accepted Answer

$x = 6$ and $x = -1$

Question 12

A scientist mixes two solutions: one with 30% salt and one with 10% salt. How many liters of each should be mixed to obtain 20 liters of a 15% salt solution?

Accepted Answer

5 liters of 30% solution and 15 liters of 10% solution

Question 13

Which of the following is the correct inverse of the function $f(x) = 3x - 4$?

Accepted Answer

$f^{-1}(x) = \frac{x + 4}{3}$

Question 14

A parabola opens upward and has vertex at $(2, -3)$. Which equation could represent this parabola?

Accepted Answer

$y = (x - 2)^2 - 3$

Question 15

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

Accepted Answer

$x < 12$

Question 16

A radioactive substance decays according to $A(t) = 200e^{-0.1t}$, where $t$ is in years. How long will it take for the substance to decay to half its original amount?

Accepted Answer

$t = \frac{\ln(0.5)}{-0.1} \approx 6.93$ years

Question 17

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

Accepted Answer

$x = 32$

Question 18

A rectangle has a length that is 3 units more than twice its width. If the perimeter is 36 units, what are the rectangle’s dimensions?

Accepted Answer

Width = 5 units, Length = 13 units

Question 19

Which of the following is the correct solution to the equation $x^2 + 4x + 5 = 0$?

Accepted Answer

$x = -2 \pm i$

Math 0031: College Algebra - Schedule and Practice Problems Overview

Study Guide - Practice Questions

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