Q: A loan of $$\5$$,000$$ is taken out at an annual interest rate of 6%, compounded quarterly. What is the value of the loan after 2 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

$$5,000 \times (1 + \frac{0.06}{4}$$)^{8}$$

Question 1

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

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$

Question 3

Which of the following equations represents an exponential decay function?

Accepted Answer

$$f(x) = 5 \cdot 0.8^x$$

Question 4

Given the function $$f(x) = 2x + 5$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$2 \cdot 9 + 5 = 23$$

Question 5

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

Accepted Answer

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

Question 6

Which of the following is the inverse of the function $$f(x) = 4x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 7}{4}$$

Question 7

A car depreciates in value by 15% each year. If the car is currently worth $$\20$$,000$, what will its value be after 3 years?

Accepted Answer

$$20,000 	imes (0.85)^3$

Question 8

Which of the following graphs represents a function?

Accepted Answer

A graph where every vertical line crosses the curve at most once

Question 9

Solve for $$x$$: $$2^{x+1} = 32$

Accepted Answer

$$x = 4$$

Question 10

A loan of $$\5$$,000$$ is taken out at an annual interest rate of 6%, compounded quarterly. What is the value of the loan after 2 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$5,000 	imes (1 + \frac{0.06}{4}$$)^{8}$$

Question 11

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

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 12

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 13

Which of the following best describes the range of the function $$f(x) = \sqrt{x - 2}$$?

Accepted Answer

All real numbers $$y \geq 0$$

Question 14

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-kt}$$. If A_0$ = 100$$ grams and $$k = 0.05$$, how much remains after 10 years?

Accepted Answer

$$100 e$$^{-0.5}$$ grams

Question 15

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

Accepted Answer

$$x = 32$$

Question 16

A geometric sequence has first term $$a_1 = 6$ and common ratio r = 2$. What is the 5th term?

Accepted Answer

$$a_5 = 96$

Question 17

Which of the following statements is true about the function $$f(x) = x^2$?

Accepted Answer

It is an even function

Question 18

A real-world application: The height $$h (in $$meters) of a ball thrown upward from the ground with an initial velocity of $$20 m/s is $$given by $$h(t) = 20t - 4.9t^2$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 19

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

Accepted Answer

$$x = 2, y = 3$$

College Algebra (MATH-120) Syllabus and Study Guide

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