Question 1

A pharmaceutical company is testing a new drug and models the concentration of the drug in the bloodstream over time with the function $$C(t) = 5e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 8 hours?

Accepted Answer

$$C(8) = 5e$$^{-1.6}$$ \approx 0.92$$

Question 2

Which of the following is the correct factorization of the polynomial $$x^3$$ - $$4x^2 + 4x$?

Accepted Answer

$$x(x-2)^2$$

Question 3

A biologist is studying population growth and models the population with the exponential function $$P(t) = 2000 \cdot 1.05^t$$, where $$t is $$the number of years. What will the population be after 10 years?

Accepted Answer

$$P(10) = 2000 \cdot 1.05$$^{10}$$ \approx 3257$$

Question 4

Which of the following is the solution set for the quadratic equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 5

A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$P(3) = 2$$ thousand dollars when $$x = 3$$

Question 6

Which of the following functions is one-to-one?

Accepted Answer

$$f(x) = 2x + 5$$

Question 7

Given the rational expression $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$, which of the following is its simplified form?

Accepted Answer

$$\frac{(x-3)(x+3)}{(x-3)^2$}$$

Question 8

A medical researcher uses the function $$f(x) = \sqrt{x-1} to $$model the reaction time (in seconds) of a patient, where $$x is $$the number of hours since medication was administered. What is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 1$$

Question 9

Convert the logarithmic equation $$\log_{2}(x) = 5 to $$its equivalent exponential form.

Accepted Answer

$$x = 2^5$

Question 10

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 11

A car rental company charges a base fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which function models the total cost $$C$$ for driving $$x$$ miles?

Accepted Answer

$$C(x) = 30 + 0.20x$$

Question 12

Simplify the radical expression $$\sqrt{50} + \sqrt{18}.$$

Accepted Answer

Question 13

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

Accepted Answer

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

Question 14

A scientist is analyzing the decay of a radioactive substance and models the amount remaining after $$t$$ years as $$A(t) = 100e$$^{-0.3t}$$. After how many years will only 20$ units remain?

Accepted Answer

$$t = \frac{\ln(5)}{0.3} \approx 5.36$$

Question 15

Which of the following is the correct simplification of $$\frac{2x^2$ - 8x}{4x}$$?

Accepted Answer

$$\frac{x-4}{2}$$

Question 16

A parabola models the path of a thrown ball: $$y = -2x^2$ + 8x + 3. $$What is the maximum height reached by the ball?

Accepted Answer

$$y = 11 at$$ $$x = 2$$

Question 17

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -2$$

Question 18

A business uses the function $$R(x) = 100x - x^2$ to model revenue, where x$ is the number of items sold. What is the maximum revenue?

Accepted Answer

$$R(50) = 2500$$

Question 19

Which of the following is the correct solution to the equation $$\sqrt{x+5} = 4$$?

Accepted Answer

$$x = 11$$

College Algebra Syllabus and Study Guide Overview

Guida di studio - Domande di pratica

Study guide - Flashcard