Question 1

Which of the following sets represents a one-to-one function?

Accepted Answer

$$\{(2, 3), (5, 4), (3, 1), (7, 8)\}$$

Question 2

Given the function $$y = \dfrac{5x-3}{2}$$, what is its inverse function?

Accepted Answer

$$y = \dfrac{2x+3}{5}$$

Question 3

A savings account has an initial deposit of $$14,000, compounded quarterly at an annual rate of 8% for 5 years. What is the future value of the account? (Use A = P(1$$+\frac{r}{n}$$)^{nt}$)

Accepted Answer

$$20,658.13$$

Question 4

Simplify $$\log_2$ 16.$$

Accepted Answer

$$4$$

Question 5

Which of the following is the correct simplification of $$\ln 2x + 3\ln x$$?

Accepted Answer

$$\ln(2x^4$)$$

Question 6

Using the change of base formula, what is $$\log_4$ 23$$ rounded to the nearest thousandth?

Accepted Answer

$$2.196$$

Question 7

If $$\log_b 3 = 0.415$$ and $$\log_b 5 = 0.568$$, what is $$\log_b 15$$?

Accepted Answer

$$0.983$$

Question 8

Solve for $$x$$: $$54x-7 = 125.$$

Accepted Answer

$$x = 1$$

Question 9

Solve the logarithmic equation: $$\log_4$ (x+3) + \log_4$ (x-3) = 2. $$Which of the following is a valid solution?

Accepted Answer

$$x = 5$$

Question 10

A car's value increased from $$8,000 in 2000 to 15$$,400 in 2015, following exponential growth. What is the value of $$k in $$the exponential growth function $$V = V_0$ e$$^{kt}$$? (Round to 4 decimal places)

Accepted Answer

$$k = 0.0430$$

Question 11

What is the doubling time for the Porsche 928's value, given $$k = 0.0430$$? (Use $$t = \frac{\ln 2}{k}$$, round to the nearest year)

Accepted Answer

$$17$$ years

Question 12

Express $$2\log x - \log 2x as a $$single logarithm and simplify.

Accepted Answer

$$\log \left(\dfrac{x}{2}\right)$$

Question 13

If $$\log_b 5 = 0.568$$ and $$\log_b 17 = 1.873$$, what is $$\log_b \dfrac{5}{17}$$?

Accepted Answer

$$-1.305$$

Question 14

Solve for $$x$$: $$2(6^{2x}) = 2592$.

Accepted Answer

$$x = 2$$

Question 15

Simplify $$\ln x + \ln(x+3) - \ln(x-5) as a $$single logarithm.

Accepted Answer

$$\ln \left(\dfrac{x(x+3)}{x-5}\right)$$

Question 16

What is the future value of an account with an initial deposit of $$21,000$$ compounding continuously at a rate of $$7.25\%$$ for $$12$$ years? (Use $$A = Pe$$^{rt}$$, round to the nearest cent)

Accepted Answer

$$48,073.13$$

Question 17

Given $$\log_7$ 343$$, what is its value?

Accepted Answer

$$3$$

Question 18

If $$\log_b 3 = 0.415$$, $$\log_b 5 = 0.568$$, and $$\log_b 17 = 1.873$$, what is $$\log_b 75$$?

Accepted Answer

$$1.551$$

Question 19

Solve for $$x$$: $$\log(x+5) - \log(x-3) = \log 2. $$Which of the following is a valid solution?

Accepted Answer

$$x = 7$$

Question 20

A person invests $$8,000 in an $$account compounding monthly at $$6.5\%$$ for $$8$$ years. What is the future value? (Use $$A = P(1+\frac{r}{n}$$)^{nt}$$, round to the nearest cent)

Accepted Answer

$$13,393.13$$

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