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

$$20,000 \times (0.85)^3$ \approx \12$$,282$

Q: A hospital monitors the temperature of a patient using the function $$T(t) = 98.6 + 0.5\sin(\frac{\pi t}{12})$$, where $$t is $$hours after midnight. What is the patient's temperature at 6 AM?

$$T(6) = 98.6 + 0.5\sin(\frac{\pi \times 6}{12}) = 98.6 + 0.5\sin(\frac{\pi}{2}) = 99.1$$

Question 1

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

Accepted Answer

A function that can be written as $$f(x) = \frac{P(x)}{Q(x)}$$ where $$P(x)$$ and $$Q(x)$$ are polynomials and $$Q(x) 
eq 0.$$

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is the value of $$f(-2)$$?

Accepted Answer

$$f(-2) = 19$$

Question 3

A chemical reaction rate $$R is $$modeled by the exponential function $$R(t) = 100e$$^{-0.05t}$$, where t$ is time in minutes. What is the reaction rate after 20 minutes?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

A population of bacteria doubles every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/4}$$

Question 6

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

Question 7

Which of the following expressions is equivalent to $$\log$$_{2}$$8$$?

Accepted Answer

$$3$$

Question 8

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

Accepted Answer

$$20,000 	imes (0.85)^3$ \approx \12$$,282$

Question 9

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 10

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 11

A hospital monitors the temperature of a patient using the function $$T(t) = 98.6 + 0.5\sin(\frac{\pi t}{12})$$, where $$t is $$hours after midnight. What is the patient's temperature at 6 AM?

Accepted Answer

$$T(6) = 98.6 + 0.5\sin(\frac{\pi 	imes 6}{12}) = 98.6 + 0.5\sin(\frac{\pi}{2}) = 99.1$$

Question 12

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

Accepted Answer

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

Question 13

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream by $$C(t) = 50e$$^{-0.2t}$$, where t$ is hours after administration. How long will it take for the concentration to drop to 10$ mg/L?

Accepted Answer

$$t = \frac{\ln(5)}{0.2} \approx 8.05$$ hours

Question 14

Which of the following is the correct solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 15

A quadratic function 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

$$h_{max} = 22.41$$ meters

Question 16

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

Accepted Answer

All real numbers except $$x = 4$$

Question 17

A business's profit $$P is $$modeled by $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold. How many units should be sold to maximize profit?

Accepted Answer

$$x = 10$$

Question 18

Which of the following is the correct solution to $$|3x - 7| = 5$$?

Accepted Answer

$$x = 4 or$$ $$x = \frac{2}{3}$$

College Algebra Syllabus and Course Structure Study Guide

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