Q: A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

$$500 \times 2$$^{3}$$ = 4000$$

Q: A car's value depreciates by 15% each year. If the car is worth $$\20$$,000$ now, what will it be worth in 3 years?

$$20,000 \times 0.85$$^{3}$$ \approx 12,282.5$$

Q: If $$f(x) = 3x - 2$$ and $$g(x) = x^2$, what is f(g(2$$))$$?

$$f(g(2)) = f(4) = 3 \times 4 - 2 = 10$$

Q: A savings account earns 6% annual interest, compounded yearly. If you deposit $$\1$$,000$, how much will you have after 5 years?

$$1,000 \times (1.06)^5$ \approx 1,338.23$$

Question 1

Which of the following best describes the purpose of an inverse function?

Accepted Answer

To reverse the effect of a function, mapping outputs back to their original inputs.

Question 2

If $$f(x) = 2x + 3$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 3}{2}$$

Question 3

A pharmaceutical company models the concentration of a drug in the bloodstream over time with $$C(t) = 5e$$^{-0.2t}$$. What is the concentration after 10 hours?

Accepted Answer

$$C(10) = 5e$$^{-2}$$ \approx 0.676$$

Question 4

Which of the following is the correct definition of a logarithmic function?

Accepted Answer

A function of the form $$f(x) = \log_b(x)$$, where $$b \u003e 0$$ and $$b 
eq 1$$

Question 5

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$500 	imes 2$$^{3}$$ = 4000$$

Question 6

Which of the following is the solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 7

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If N_0$ = 1000$$ and $$k = 0.05$$, how much remains after 20 years?

Accepted Answer

$$N(20) = 1000 e$$^{-1}$$ \approx 367.9$$

Question 8

Which of the following is the correct domain for the function $$f(x) = \sqrt{x - 4}$$?

Accepted Answer

$$x \geq 4$$

Question 9

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

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 10

A car's value depreciates by 15% each year. If the car is worth $$\20$$,000$ now, what will it be worth in 3 years?

Accepted Answer

$$20,000 	imes 0.85$$^{3}$$ \approx 12,282.5$$

Question 11

Which of the following is the range of the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

All real numbers except $$0$$

Question 12

If $$f(x) = 3x - 2$$ and $$g(x) = x^2$, what is f(g(2$$))$$?

Accepted Answer

$$f(g(2)) = f(4) = 3 	imes 4 - 2 = 10$$

Question 13

A savings account earns 6% annual interest, compounded yearly. If you deposit $$\1$$,000$, how much will you have after 5 years?

Accepted Answer

$$1,000 	imes (1.06)^5$ \approx 1,338.23$$

Question 14

Which of the following is the solution to $$e^{x} = 7$?

Accepted Answer

$$x = \ln(7)$$

Question 15

If $$f(x) = \log_{10}(x)$$, what is $$f(1000)$$?

Accepted Answer

$$f(1000) = 3$$

Question 16

A chemical reaction follows $$C(t) = 100e$$^{-0.1t}$$. How long will it take for the concentration to drop to 25$?

Accepted Answer

$$t = \frac{\ln(0.25)}{-0.1} \approx 13.86$$

Question 17

Which of the following is the correct solution to $$2^{x} = 64$?

Accepted Answer

$$x = 6$$

Question 18

If $$f(x) = \sqrt{x}$$ and $$g(x) = x + 4$$, what is $$(f \circ g)(5)$$?

Accepted Answer

$$(f \circ g)(5) = f(g(5)) = f(9) = 3$$

Question 19

A city’s population grows exponentially according to $$P(t) = 50,000e$$^{0.03t}$$. What is the population after 10 years?

Accepted Answer

$$P(10) = 50,000e$$^{0.3}$$ \approx 67,965$$

Precalculus Course Syllabus and Weekly Topic Overview

Guida di studio - Domande di pratica

Study guide - Flashcard