Q: A chemical reaction is modeled by $$C(t) = 100 - 80e$$^{-0.5t}$$, where C$ is the concentration in mg/L after t$ hours. What is the initial concentration?

$$C(0) = 100 - 80 \times 1 = 20 mg/L$$

Q: A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

$$V(3) = 20000 \times 0.85^3$ \approx 12251$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq 2.5$$

Question 2

A biologist models the population of a bacteria culture with the exponential function $$P(t) = 500e$$^{0.3t}$$, where t$ is measured in hours. What is the population after 4 hours?

Accepted Answer

$$P(4) = 500e$$^{1.2}$$ \approx 1660$$

Question 3

Which of the following is the inverse function of $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 4

A projectile is launched from the ground and its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 24t. $$What is the maximum height reached by the projectile?

Accepted Answer

$$h_{max} = 58.8$$ meters

Question 5

Which of the following is a solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 6

Given the quadratic function $$f(x) = x^2$ - 6x + 8$$, what are the zeros of the function?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 7

Which of the following graphs represents a function that is one-to-one?

Accepted Answer

A straight line with positive slope

Question 8

A chemical reaction is modeled by $$C(t) = 100 - 80e$$^{-0.5t}$$, where C$ is the concentration in mg/L after t$ hours. What is the initial concentration?

Accepted Answer

$$C(0) = 100 - 80 	imes 1 = 20 mg/L$$

Question 9

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 10

A car's value depreciates according to $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

Accepted Answer

$$V(3) = 20000 	imes 0.85^3$ \approx 12251$$

Question 11

Which of the following is the solution set for the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following is the sum of the first five terms of the arithmetic sequence with $$a_1 = 3$ and d = 4$?

Accepted Answer

$$S_5 = 3 + 7 + 11 + 15 + 19 = 55$

Question 14

A business's revenue is modeled by $$R(x) = -2x^2$ + 120x$$, where $$x is $$the number of units sold. What is the number of units that maximizes revenue?

Accepted Answer

$$x = 60$$

Question 15

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 1$$

Question 16

Which of the following is the sum of the infinite geometric series $$\sum_{n=0}^{\infty} 5 \left(\frac{1}{3}\right)^n$$?

Accepted Answer

$$\frac{5}{1 - \frac{1}{3}} = \frac{5}{\frac{2}{3}} = 7.5$$

Question 17

Which of the following is the correct solution to $$\log_{2}(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 18

A medication's concentration in the bloodstream decreases according to $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. After how many hours will the concentration be half its initial value?

Accepted Answer

$$t = \frac{\ln(0.5)}{-0.2} \approx 3.47$$ hours

Question 19

Which of the following is the correct solution to the equation $$x^2 + 4x + 5 = 0$?

Accepted Answer

$$x = -2 \pm i$$

Precalculus Study Guide: Functions, Graphs, and Equations

Study Guide - Practice Questions

Study Guide - Flashcards