Question 1

Which of the following best describes the concept of a function as studied in College Algebra?

Accepted Answer

A relationship where each input is paired with exactly one output.

Question 2

A biologist is modeling the population growth of a bacteria culture using the function $$P(t) = 500e$$^{0.3t}$$, where t$ is measured in hours. What type of function is this, and what does the constant 0.3$ represent?

Accepted Answer

Exponential function; $$0.3 is $$the growth rate.

Question 3

Which equation represents a linear equation in two variables?

Accepted Answer

$$2x + 3y = 7$$

Question 4

A company’s revenue $$R (in $$thousands of dollars) is modeled by the quadratic function $$R(x) = -2x^2$ + 40x + 100$$, 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 $$500$$ thousand dollars at $$x = 10$$ thousand units.

Question 5

Which of the following is the solution set to the inequality $$3x - 5 \u003c 10$$?

Accepted Answer

$$x \u003c 5$$

Question 6

A system of equations is given by $$\begin{cases} 2x + y = 8 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(3, 2)$$

Question 7

Which of the following best describes the graph of the equation $$x^2$$ + $$y^2 = 25$?

Accepted Answer

A circle with center at $$(0, 0)$$ and radius $$5.$$

Question 8

A pharmacist needs to mix a $$10\%$$ saline solution with a $$30\%$$ saline solution to obtain $$100 mL of a$$ $$25\%$$ saline solution. How many mL of the $$30\%$$ solution should be used?

Accepted Answer

$$75 mL$$

Question 9

Which of the following is equivalent to $$\log_{2} 32$$?

Accepted Answer

$$5$$

Question 10

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

Accepted Answer

$$19$$

Question 11

A quadratic equation $$ax^2 + bx + c = 0$ has real and equal roots. Which condition must be satisfied?

Accepted Answer

$$b^2 - 4ac = 0$

Question 12

Which of the following is the correct solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 13

A student invests $$\1000$ in an account that earns 6$$\%$$ annual interest compounded yearly. What will be the value of the investment after 3$ years? (Round to the nearest dollar.)

Accepted Answer

$$1191$$

Question 14

Which of the following expressions is undefined for $$x = 2$$?

Accepted Answer

$$\dfrac{1}{x-2}$$

Question 15

A matrix $$A is $$given by $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}. $$What is the determinant of $$A$$?

Accepted Answer

$$-2$$

Question 16

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

$$(3, 2)$$

Question 17

Which of the following is the correct domain of the function $$f(x) = \dfrac{1}{x^2$ - 9}$$?

Accepted Answer

$$x 
eq 3$$ and $$x 
eq -3$$

Question 18

A real-world application: A medical researcher is studying the decay of a drug in the bloodstream, modeled by $$C(t) = 50e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5$ hours? (Round to the nearest mg/L.)

Accepted Answer

$$18 mg/L$$

Question 19

Which of the following statements about logarithmic and exponential functions is true?

Accepted Answer

The function $$y = \log_b x is $$the inverse of $$y = b^x.$$

College Algebra Syllabus and Course Structure Study Guide

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