Question 1

Solve the absolute value inequality $$|2x - 6| \leq 8$$ and express your answer in interval notation.

Accepted Answer

$$[-1, 7]$$

Question 2

A biologist is tracking the population of a rare plant, which grows according to the exponential model $$P(t) = 1200e$$^{0.03t}$$, where t$ is in years. What will the population be after 5 years, rounded to the nearest whole number?

Accepted Answer

$$1397$$

Question 3

Rewrite the equation $$4x - 2y = 10 in $$slope-intercept form and identify the slope.

Accepted Answer

Slope-intercept form: $$y = 2x - 5$$, slope $$2$$

Question 4

Solve the logarithmic equation $$\log_5$(x - 2) = 3$$ for $$x.$$

Accepted Answer

$$x = 127$$

Question 5

A savings account earns compound interest at a rate of $$4\%$$ per year, compounded quarterly. If $$P = 5000$$ and $$t = 3$$ years, what is the account balance $$A$$ after 3 years? (Round to the nearest cent.)

Accepted Answer

$$A = 5631.36$$

Question 6

Find the domain of the function $$f(x) = \log_{10}(2x - 4).$$

Accepted Answer

$$(2, \infty)$$

Question 7

Solve the equation $$(x - 3$$)^{2/5}$$ = 32$$ for $$x.$$

Accepted Answer

$$x = 35$$ and $$x = -29$$

Question 8

Express $$\dfrac{5}{2 + 3i} in $$standard complex form $$a + bi.$$

Accepted Answer

$$\dfrac{10}{13} + \dfrac{15}{13}i$$

Question 9

Given $$f(x) = x^2$ + 1$$ and $$g(x) = 2x - 3$$, find $$(f \circ g)(2).$$

Accepted Answer

$$26$$

Question 10

A medical researcher models the spread of a virus with $$N(t) = 5000e$$^{0.07t}$$, where N$ is the number of cases and t$ is days. How many cases will there be after 10 days? (Round to the nearest whole number.)

Accepted Answer

$$10035$$

Question 11

Solve the system of equations: $$y = 2x + 3$$ and $$4x - 2y = 6. $$What is the solution?

Accepted Answer

$$(3, 9)$$

Question 12

Which of the following is the range of the function $$f(x) = (x - 2)^2$ - 5$$?

Accepted Answer

$$[-5, \infty)$$

Question 13

A chemical reaction is modeled by $$C(t) = 2000(1 + 0.08/12$$)^{12t}$$, where C$ is the concentration after t$ years. What is C$ after 2 years? (Round to the nearest whole number.)

Accepted Answer

$$2337$$

Question 14

Find the slope of the line passing through the points $$(4, 7)$$ and $$(10, -5).$$

Accepted Answer

$$-2$$

Question 15

Solve the equation $$\log_3$(x) + \log_3$(x - 2) = 1$$ for $$x.$$

Accepted Answer

$$x = 3$$

Question 16

A parabola $$f(x) = (x + 2)^2$ - 7$$ opens upward. What is its vertex and axis of symmetry?

Accepted Answer

Vertex $$(-2, -7)$$, axis $$x = -2$$

Question 17

Which interval notation represents all real numbers $$x$$ such that $$x \geq 5$$?

Accepted Answer

$$[5, \infty)$$

Question 18

If $$f(x) = \log_2$(x)$$ and $$g(x) = 2^x$$, which statement is true about their graphs?

Accepted Answer

They are inverses and reflect across $$y = x$$

Question 19

Solve the equation $$(x + 5)^2$ = -36$$ over the complex numbers.

Accepted Answer

$$x = -5 \pm 6i$$

College Algebra Final Exam Study Guide: Key Concepts and Examples

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