Q: A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

$$P(t) = 500 \times 2$$^{t/3}$$

Q: A car’s value $$V$$ depreciates exponentially according to $$V(t) = 20000 \times 0.85^t$$, where $$t is $$years after purchase. What is the value after 5 years?

$$V(5) = 20000 \times 0.85^5$ \approx 8867$$

Question 1

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

Accepted Answer

A function that can be expressed as the ratio of two polynomials, where the denominator is not zero.

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 3

A chemical reaction's rate $$R is $$modeled by the exponential function $$R(t) = 5e$$^{-0.2t}$$, where t$ is time in minutes. What is the rate after 10 minutes?

Accepted Answer

$$R(10) = 5e$$^{-2}$$ \approx 0.68$$

Question 4

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

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 5

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 	imes 2$$^{t/3}$$

Question 6

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

Accepted Answer

$$x 
eq 4$$

Question 7

A student is analyzing the graph of $$y = \log_2$(x-1). $$Which of the following statements is true about its domain?

Accepted Answer

$$x \u003e 1$$

Question 8

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward: $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$24.4$$ meters

Question 9

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

Accepted Answer

$$x = 4$$

Question 10

A medical test result is modeled by the function $$f(x) = 3x^2$ - 12x + 15. $$For what value of $$x$$ does the minimum occur?

Accepted Answer

$$x = 2$$

Question 11

Which of the following is the correct inverse of the function $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 12

A company’s profit $$P in $$thousands of dollars is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$P = 32$$ thousand dollars

Question 13

Which of the following is the correct solution to $$\log_3$(x) = 4$$?

Accepted Answer

$$x = 81$$

Question 14

A quadratic equation $$ax^2 + bx + c = 0$ has real solutions if and only if:

Accepted Answer

$$b^2 - 4ac$$ \geq 0$$

Question 15

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$. How much remains after 20 years?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.79$$

Question 16

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

$$(x, y) = (3, 1)$$

Question 17

Which of the following is the correct solution to $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 18

A car’s value $$V$$ depreciates exponentially according to $$V(t) = 20000 	imes 0.85^t$$, where $$t is $$years after purchase. What is the value after 5 years?

Accepted Answer

$$V(5) = 20000 	imes 0.85^5$ \approx 8867$$

Question 19

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

Accepted Answer

$$x = 2 ($$double root)

College Algebra: Course Overview and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드