Q: A car’s value depreciates exponentially according to $$V(t) = 20000 \times 0.85^t$$, where $$t is $$the number of years. What is the value after 3 years?

$$V(3) = 20000 \times 0.85^3$ \approx 12262.5$$

Question 1

Which of the following is the correct solution set for the inequality $$2x - 5 \u003e 7$$?

Accepted Answer

$$x \u003e 6$$

Question 2

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

Accepted Answer

$$2x^2 + 3$

Question 3

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

Accepted Answer

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

Question 4

A company’s profit $$P (in $$dollars) from selling $$x$$ units is modeled by $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

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

Question 5

Which of the following is the graph of a quadratic equation?

Accepted Answer

A parabola

Question 6

Solve the equation $$\frac{3}{x} = 6$$ for $$x.$$

Accepted Answer

$$x = 0.5$$

Question 7

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 2$$

Question 8

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-0.03t}$$, where A_0$ is the initial amount. What is the amount left after 50$ years if A_0$ = 100$$ grams?

Accepted Answer

$$A(50) = 100e$$^{-1.5}$$ \approx 22.31$$ grams

Question 9

Which of the following is the correct solution to $$\log_{2}(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 10

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

Accepted Answer

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

Question 11

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 1 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 12

A population of bacteria triples every 4 hours. If the initial population is 200, what is the population after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 13

Which of the following is the correct solution to the radical equation $$\sqrt{x + 5} = 4$$?

Accepted Answer

$$x = 11$$

Question 14

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Question 15

If $$f(x) = 2x + 1$$ and $$g(x) = x - 3$$, what is $$(f + g)(x)$$?

Accepted Answer

$$3x - 2$$

Question 16

Which of the following equations represents a line passing through the points $$(1,2)$$ and $$(3,6)$$?

Accepted Answer

$$y = 2x$$

Question 17

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

Accepted Answer

$$x = 4$$

Question 18

Which of the following is the correct solution to the rational equation $$\frac{x}{x-1} = 2$$?

Accepted Answer

$$x = 2$$

Question 19

A car’s value depreciates exponentially according to $$V(t) = 20000 	imes 0.85^t$$, where $$t is $$the number of years. What is the value after 3 years?

Accepted Answer

$$V(3) = 20000 	imes 0.85^3$ \approx 12262.5$$

College Algebra (MAT1313) Syllabus and Course Overview

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