Question 1

Solve the quadratic equation $$x^2 - 4x$$ \leq 0$$.

Accepted Answer

$$0 \leq x \leq 4$$

Question 2

Which of the following is the correct solution set for $$x^2 - 5x - 8$$ \u003c 0$$?

Accepted Answer

$$-1.12 \u003c x \u003c 7.12$$

Question 3

Solve the inequality $$x^2 - 5$$ \u003e 0$$.

Accepted Answer

$$x  \sqrt{5}$$

Question 4

Approximate $$2^4.7$ using a calculator.

Accepted Answer

$$25.99$$

Question 5

Which of the following is the correct graph for $$f(x) = 2^x$$?

Accepted Answer

An exponential curve increasing from left to right, passing through $$(0,1)$$

Question 6

Given $$P = 12,000$$, which yields a greater return over 10 years: $$6\%$$ compounded annually or $$5.8\%$$ compounded continuously?

Accepted Answer

$$6\%$$ compounded annually

Question 7

Which of the following is the correct formula for continuous compounding?

Accepted Answer

$$A = Pe$$^{rt}$$

Question 8

Simplify $$\log_2$ 8.$$

Accepted Answer

$$3$$

Question 9

Expand $$\log \left( \frac{x}{y} \right).$$

Accepted Answer

$$\log x - \log y$$

Question 10

Condense $$\log 3 + 2\log 4 - \log 5$$ into a single logarithm.

Accepted Answer

$$\log \left( \frac{3 \cdot 16}{5} \right)$$

Question 11

Use the change of base formula to evaluate $$\log_5$ 8 to $$four decimal places.

Accepted Answer

$$\frac{\ln 8}{\ln 5} \approx 1.2925$$

Question 12

Solve for $$x$$: $$9^{x+1}$$ = $$27^{x-2}.$$

Accepted Answer

$$x = 5$$

Question 13

Evaluate $$\log_{10} (2x) + \log_{10} (5x).$$

Accepted Answer

$$\log_{10} (10x^2$)$$

Question 14

If $$f(x) = 3^x$$ and $$g(x) = 3$$^{x-2}$$, which of the following is true?

Accepted Answer

$$g(x) = \frac{f(x)}{9}$$

Question 15

Which of the following is equivalent to $$\log_b a^k$$?

Accepted Answer

$$k \log_b a$$

Question 16

Solve for $$x$$: $$e^{2x} = 7$.

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 17

Which of the following best describes the domain of $$f(x) = \log(x-2)$$?

Accepted Answer

$$x \u003e 2$$

Question 18

If $$A = P(1 + r/n$$)^{nt}$$, what does n$ represent in the context of compound interest?

Accepted Answer

The number of compounding periods per year

Question 19

Which of the following is the correct expansion for $$\log(x^2$y^3$$)$?

Accepted Answer

$$2\log x + 3\log y$$

Question 20

A medical researcher is modeling the growth of bacteria using $$N(t) = N_0$ e$$^{kt}$$. If the initial population is 500$ and the population doubles in 3$ hours, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{3}$$

College Algebra Exam 3 Review Guidance

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