Q: A car's value $V$ depreciates exponentially according to $V(t) = 20000 \times (0.85)^t$, where $t$ is the number of years since purchase. What is the value after 5 years?

$V(5) = 20000 \times (0.85)^5 \approx 8863$

Q: A biologist models the growth of a plant with $h(t) = 2t^2 + 3t + 1$, where $h$ is height in cm and $t$ is time in weeks. What is the height after 4 weeks?

$h(4) = 2 \times 16 + 3 \times 4 + 1 = 32 + 12 + 1 = 45$ cm

Q: A city’s population $P$ grows according to $P(t) = 10000 \times e^{0.03t}$, where $t$ is years since 2000. What is the population in 2020?

$P = 10000 \times e^{0.6} \approx 18211$

Q: Which of the following is the correct solution to $\sin(\theta) = 0.5$ for $0 \leq \theta < 360^{\circ}$?

$\theta = 30^{\circ}$ and $150^{\circ}$

Question 1

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

Accepted Answer

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

Question 2

A chemical reaction's rate $R$ is modeled by the function $R(t) = 5e^{-0.2t}$, where $t$ is time in minutes. What is the rate after 10 minutes?

Accepted Answer

$R(10) = 5e^{-2} \approx 0.68$

Question 3

Which of the following equations represents a line with slope $m = -3$ and $y$-intercept $b = 5$?

Accepted Answer

$y = -3x + 5$

Question 4

A hospital tracks the number of patients $P$ admitted each day using the quadratic model $P(d) = -2d^2 + 20d + 50$, where $d$ is the day of the month. On which day is the maximum number of patients admitted?

Accepted Answer

$d = 10$

Question 5

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

Accepted Answer

$x = 0$ and $x = 4$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is $P_0 = 500$, what is the population after 9 hours?

Accepted Answer

$P = 500 	imes 2^3 = 4000$

Question 7

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

Accepted Answer

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

Question 8

A car's value $V$ depreciates exponentially according to $V(t) = 20000 	imes (0.85)^t$, where $t$ is the number of years since purchase. What is the value after 5 years?

Accepted Answer

$V(5) = 20000 	imes (0.85)^5 \approx 8863$

Question 9

Which of the following is the solution set for $|x - 4| = 7$?

Accepted Answer

$x = -3$ and $x = 11$

Question 10

A medication's concentration $C$ in the bloodstream is modeled by $C(t) = 100e^{-0.5t}$, where $t$ is in hours. How long until the concentration drops to $25$ mg/L?

Accepted Answer

$t = 2.77$ hours

Question 11

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

Question 12

A company’s profit $P$ is given by $P(x) = -4x^2 + 40x - 36$, where $x$ is the number of units sold. What is the maximum profit?

Question 13

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 14

A biologist models the growth of a plant with $h(t) = 2t^2 + 3t + 1$, where $h$ is height in cm and $t$ is time in weeks. What is the height after 4 weeks?

Accepted Answer

$h(4) = 2 	imes 16 + 3 	imes 4 + 1 = 32 + 12 + 1 = 45$ cm

Question 15

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

Accepted Answer

$x = 32$

Question 16

A city’s population $P$ grows according to $P(t) = 10000 	imes e^{0.03t}$, where $t$ is years since 2000. What is the population in 2020?

Accepted Answer

$P = 10000 	imes e^{0.6} \approx 18211$

Question 17

Which of the following is the correct solution to $x^2 + 6x + 9 = 0$?

Accepted Answer

$x = -3$

Question 18

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 20% salt solution?

Accepted Answer

5 liters of 30% and 15 liters of 10%

Question 19

Which of the following is the correct solution to $\sin(	heta) = 0.5$ for $0 \leq 	heta < 360^{\circ}$?

Accepted Answer

$	heta = 30^{\circ}$ and $150^{\circ}$

Math 1030 College Algebra Syllabus and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards