Question 1

Which of the following is the correct equation for the inverse of the function $$y = 5x - 8$$?

Accepted Answer

$$x = 5y - 8$$

Question 2

A pharmaceutical company uses the formula $$P = 600 \cdot 2$$^{-0.4n}$$ to model the amount of particulate matter left after n$ filtering steps. What is the amount left after 5 filtering steps, rounded to the nearest whole number?

Accepted Answer

$$150$$ units

Question 3

Which of the following is the correct inverse function for $$f(x) = 1/(4x + 6)$$?

Accepted Answer

$$f^{-1}(x) = 4x - 24$

Question 4

A $1000 investment appreciates for 4 years at 14% interest, compounded semiannually. What is the account balance at the end of the period?

Accepted Answer

$$1718.19$$

Question 5

Convert the exponential equation $$e^5 = t$ to its logarithmic form.

Accepted Answer

$$\ln t = 5$$

Question 6

What is the value of $$\log_2$ 16$$?

Accepted Answer

$$4$$

Question 7

Express $$\ln(x^2$ - 4) - \ln(x + 2) as a $$single logarithm and simplify if possible.

Accepted Answer

$$\ln(x - 2)$$

Question 8

A population grows according to $$F(t) = 400 \log(2t + 3)$$, where $$t is $$months since introduction. What is the population after 6 months?

Accepted Answer

$$470$$

Question 9

Which of the following is the correct logarithmic equation for $$4^2 = 16$?

Accepted Answer

$$\log_4$ 16 = 2$$

Question 10

If the population of a country doubles in 15.40 years, what is the exponential growth rate $$k ($$rounded to the nearest tenth of a percent)?

Accepted Answer

$$4.5\%$$

Question 11

Simplify $$\log_a a^2$.

Accepted Answer

$$2$$

Question 12

What is the doubling time for an investment of $$5000 at an $$interest rate of $$5.1\%$$ per year, compounded continuously?

Accepted Answer

$$13.6$$ years

Question 13

Solve the exponential equation $$4^{9 - 3x} = 64$. What is the value of x$?

Accepted Answer

$$2$$

Question 14

Find the value of $$\log_2$ \frac{1}{128}.$$

Accepted Answer

$$-7$$

Question 15

Express $$\log_a 0.1 + \log_a 100 as a $$single logarithm and simplify.

Accepted Answer

$$\log_a 10$$

Question 16

A country has an annual population growth rate of $$1.7\%. $$How long will it take for the population to double? (Round to the nearest year.)

Accepted Answer

$$41$$ years

Question 17

Which of the following is the correct exponential equation for $$\log_7$ 49 = 2$$?

Accepted Answer

$$7^2 = 49$

Question 18

Use the change-of-base formula to find $$\log_{200} 40. $$Which value is closest?

Accepted Answer

$$0.6962$$

Question 19

Simplify $$10 \log t.$$

Accepted Answer

$$t$$

Question 20

Express $$\frac{1}{2} \ln x - \ln 3 as a $$single logarithm.

Accepted Answer

$$\ln \frac{\sqrt{x}}{3}$$

Precalculus Chapter 5: Inverses, Exponentials, and Logarithms – Guided Study

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