Question 1

Which of the following best describes the primary purpose of College Algebra as outlined in the course syllabus?

Accepted Answer

To foster mathematical modeling, problem-solving, and critical thinking skills with applications in real-world and non-STEM contexts.

Question 2

A biologist is modeling the population growth of a species using the function $$P(t) = 500 \cdot 2$$^{0.3t}$$, where t$ is measured in years. What is the population after 5 years?

Accepted Answer

$$P(5) = 500 \cdot 2$$^{1.5}$$ = 500 \cdot 2.828 = 1414$$

Question 3

Which of the following equations represents a line with a slope of $$-3$$ and a $$y-$$intercept of $$4$$?

Accepted Answer

$$y = -3x + 4$$

Question 4

A company’s profit $$P (in $$thousands of dollars) is modeled by the quadratic function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units (in thousands) produced. What is the maximum profit, and how many units should be produced to achieve it?

Accepted Answer

Maximum profit is $$P(2) = -2(2)^2$ + 8(2) + 10 = 18 at$$ $$x = 2$$ thousand units.

Question 5

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 6

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-0.05t}$$, where A_0$ is the initial amount and t$ is time in years. If A_0$ = 100$$ grams, how much remains after 10 years? (Round to the nearest gram.)

Accepted Answer

$$A(10) = 100 e$$^{-0.5}$$ \approx 100 \cdot 0.6065 = 61$$ grams

Question 7

Which of the following best describes the graph of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

It is a hyperbola with a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0.$$

Question 8

A student is analyzing the function $$g(x) = 3x^2$ - 12x + 7. $$What are the coordinates of the vertex of this parabola?

Accepted Answer

$$(2, -5)$$

Question 9

If the probability of a machine failing on any given day is $$0.02$$, what is the probability that it will not fail over a 5-day work week?

Accepted Answer

$$(1 - 0.02)^5$ = 0.9039$$

Question 10

Which of the following is the correct solution to the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 11

A chemist mixes two solutions: one with 30% acid and another with 50% acid. How many liters of each should be mixed to obtain 10 liters of a 42% acid solution?

Accepted Answer

4 liters of 30% solution and 6 liters of 50% solution

Question 12

Which of the following is the correct logarithmic form of the exponential equation $$5^x = 125$$?

Accepted Answer

$$\log_5$ 125 = x$$

Question 13

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

Accepted Answer

$$V(3) = 20000 \cdot (0.85)^3$ = 20000 \cdot 0.6141 = 12282$$

Question 14

Which of the following is the correct solution set for the equation $$|3x - 7| = 5$$?

Accepted Answer

$$x = 4, x = \frac{2}{3}$$

Question 15

A student is using a graphing calculator to solve the equation $$x^2 - 6x + 8 = 0$. What are the solutions?

Accepted Answer

$$x = 2, x = 4$$

Question 16

Which of the following best describes the end behavior of the function $$f(x) = -2x^3$ + 5x^2$ - x + 7 as$$ $$x 	o \infty$$?

Accepted Answer

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

Question 17

A hospital administrator is scheduling nurses for shifts. If there are 6 nurses and 3 shifts to fill, how many different ways can the shifts be assigned if each nurse can work only one shift?

Accepted Answer

$$6 	imes 5 	imes 4 = 120$$

Question 18

Which of the following is the correct domain of the function $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

$$x \geq 3$$

Question 19

A student is asked to solve the system of inequalities: $$\begin{cases} y \u003e 2x - 1 \ y \leq -x + 4 \end{cases}. $$Which of the following points is in the solution set?

Accepted Answer

$$(1, 3)$$

College Algebra (Math 1710) – Course Structure, Topics, and Study Guide

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