Q: Which of the following is the correct definition of a logarithmic function?

$f(x) = \log_b(x)$,\ where\ b > 0,\ b \neq 1,\ x > 0$

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

$x \in \mathbb{R},\ x \neq 3,\ x \neq -3$

Q: A loan of $10,000 is taken out at an annual interest rate of 6\% compounded monthly. What is the amount owed after 3 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

$A = 10,000 \times (1 + \frac{0.06}{12})^{36} \approx 11,972.80$

Q: A car depreciates in value by 15\% each year. If the car is currently worth $20,000, what will its value be after 4 years?

$20,000 \times (0.85)^4 \approx 10,443$

Q: A savings account earns 5\% annual interest, compounded quarterly. If you deposit $2,000, how much will you have after 6 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

$A = 2,000 \times (1 + \frac{0.05}{4})^{24} \approx 2,691.59$

Question 1

A pharmaceutical company models the decay of a drug in the bloodstream using the function $C(t) = C_0 e^{-0.2t}$, where $C_0$ is the initial concentration and $t$ is time in hours. If the initial concentration is 100 mg/L, what is the concentration after 5 hours?

Accepted Answer

$C(5) = 100 e^{-1} \approx 36.79$ mg/L

Question 2

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

Accepted Answer

$f(x) = \log_b(x)$,\ where\ b > 0,\ b 
eq 1,\ x > 0$

Question 3

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $P(t)$ after $t$ hours?

Accepted Answer

$P(t) = 200 	imes 3^{t/4}$

Question 4

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

Accepted Answer

$x \in \mathbb{R},\ x 
eq 3,\ x 
eq -3$

Question 5

A loan of $10,000 is taken out at an annual interest rate of 6\% compounded monthly. What is the amount owed after 3 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

Accepted Answer

$A = 10,000 	imes (1 + \frac{0.06}{12})^{36} \approx 11,972.80$

Question 6

Which of the following equations is equivalent to $\log_2(x) = 5$?

Accepted Answer

$x = 2^5$

Question 7

A company’s revenue $R(x)$ in thousands of dollars is modeled by $R(x) = -2x^2 + 12x + 20$, where $x$ is the number of units sold in thousands. What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $R(3) = 38$ thousand dollars, at $x = 3$ thousand units

Question 8

Which of the following is the correct solution to the equation $2^{x+1} = 16$?

Accepted Answer

$x = 3$

Question 9

A chemical reaction follows the law $A = A_0 e^{-kt}$. If $A_0 = 50$ grams and $A = 25$ grams after 10 minutes, what is the value of $k$?

Accepted Answer

$k = \dfrac{\ln(2)}{10}$

Question 10

Which of the following is the correct inverse of the function $f(x) = 5x - 7$?

Accepted Answer

$f^{-1}(x) = \dfrac{x+7}{5}$

Question 11

A car depreciates in value by 15\% each year. If the car is currently worth $20,000, what will its value be after 4 years?

Accepted Answer

$20,000 	imes (0.85)^4 \approx 10,443$

Question 12

Which of the following is the correct solution to the equation $\log_3(x) + \log_3(x-2) = 2$?

Accepted Answer

$x = 3$

Question 13

A rational function has a vertical asymptote at $x = 2$ and a horizontal asymptote at $y = 0$. Which of the following could be its equation?

Accepted Answer

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

Question 14

If $f(x) = x^2 - 4x + 3$, what is the vertex of the parabola?

Accepted Answer

Vertex at $(2, -1)$

Question 15

A savings account earns 5\% annual interest, compounded quarterly. If you deposit $2,000, how much will you have after 6 years? (Use $A = P(1 + \frac{r}{n})^{nt}$)

Accepted Answer

$A = 2,000 	imes (1 + \frac{0.05}{4})^{24} \approx 2,691.59$

Question 16

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 17

Which of the following is the correct factorization of $x^3 - 8$?

Accepted Answer

$(x - 2)(x^2 + 2x + 4)$

Question 18

A radioactive substance decays according to $N(t) = N_0 e^{-0.05t}$. If the initial amount is 500 grams, how long will it take for the substance to decay to 100 grams?

Accepted Answer

$t = \dfrac{\ln(0.2)}{-0.05} \approx 32.19$ years

Question 19

Which of the following is the correct solution to the equation $\dfrac{3}{x} + 2 = 5$?

Accepted Answer

$x = 1$

College Algebra Syllabus and Course Structure: Key Topics and Policies

Study Guide - Practice Questions

Study Guide - Flashcards