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

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

Q: A car's value depreciates by 15% each year. If the car is currently worth $$\20$$,000$, what will its value be after 3 years? (Round to the nearest dollar.)

$$V = 20000 \times (0.85)^3$ \approx \12$$,281$

Question 1

Which of the following best describes the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 2

A pharmaceutical company models the concentration $$C (in mg/L) of a $$drug in the bloodstream $$t$$ hours after injection by $$C(t) = 5e$$^{-0.4t}$$. What is the concentration after 3 hours? (Round to two decimal places.)

Accepted Answer

$$C(3) = 5e$$^{-1.2}$$ \approx 1.51 mg/L$$

Question 3

Which of the following is the solution set for the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 4

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 5

Which of the following is the inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x-5}{2}$$

Question 6

A quadratic function models the height $$h (in $$meters) of a ball thrown upward from a building: $$h(t) = -4.9t^2$ + 19.6t + 50. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 7

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 8

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x-4)(x-5)$$

Question 9

A car's value depreciates by 15% each year. If the car is currently worth $$\20$$,000$, what will its value be after 3 years? (Round to the nearest dollar.)

Accepted Answer

$$V = 20000 	imes (0.85)^3$ \approx \12$$,281$

Question 10

Which of the following is the solution to the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 11

A chemical reaction follows the equation $$A = A_0$ e$$^{-kt}$$, where A_0$ is the initial amount and k$ is a positive constant. If A_0$ = 100$$ grams, $$k = 0.2$$, how much remains after 5 hours? (Round to the nearest gram.)

Accepted Answer

$$A = 100e$$^{-1}$$ \approx 37$$ grams

Question 12

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

Accepted Answer

$$x = 32$$

Question 13

A company’s revenue $$R (in $$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 $$R(3) = 38 at$$ $$x = 3$$ thousand units

Question 14

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

Accepted Answer

$$x = 7,\ x = -2$$

Question 15

A student invests $$\1$$,000$ in an account that pays 6% annual interest compounded quarterly. What will the balance be after 2 years? (Round to the nearest dollar.)

Accepted Answer

$$A = 1000 \left(1 + \dfrac{0.06}{4}\$$right)^{8}$$ \approx \1$$,127$

Question 16

Which of the following is the solution to the equation $$x^2 + 4x + 8 = 0$?

Accepted Answer

$$x = -2 \pm 2i$$

Question 17

A rectangle has a length that is 3 meters more than twice its width. If the area is $$33$$ square meters, what is the width?

Accepted Answer

$$3$$ meters

Question 18

Which of the following is the solution to the system of equations $$\begin{cases} x + y = 8 \ x - y = 2 \end{cases}$$?

Accepted Answer

$$x = 5,\ y = 3$$

Question 19

If $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$3$$

Question 20

A cell phone plan charges a base fee of $$\25$ per month plus $$\$$0.10$$ per text message. Which equation models the monthly cost $$C$$ for $$n$$ text messages?

Accepted Answer

$$C = 25 + 0.10n$$

College Algebra (MATH-1314) Course Overview and Study Guide

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