Q: A medical researcher models the spread of a virus by $$V(t) = 100e$$^{0.2t}$$. What is the approximate value of V(5$$)$$? (Use e$$^{1}$$ \approx 2.718)$$

$$V(5) = 100e$$^{1}$$ \approx 100 \times 2.718 = 271.8$$

Q: A quadratic function models the height of a ball thrown upward: $$h(t) = -16t^2$ + 32t + 5. $$What is the maximum height reached by the ball?

The maximum occurs at $$t = -\frac{b}{2a} = -\frac{32}{2 \times -16} = 1$$. $$h(1) = -16(1)^2$ + 32(1) + 5 = -16 + 32 + 5 = 21$$ feet.

Q: Which of the following is the correct simplification of $$\sqrt{50}$$?

$$\sqrt{25 \times 2} = 5\sqrt{2}$$

Q: A hospital records the number of patients admitted each day as $$N(d) = 12d + 5. If 10 $$days have passed, how many patients have been admitted in total?

$$N(10) = 12 \times 10 + 5 = 120 + 5 = 125$$

Q: A scientist models the temperature of a reaction by $$T(t) = 20 + 5\sin(\frac{\pi}{6}t)$$, where $$t is $$time in minutes. What is the temperature at $$t = 6$$ minutes?

$$T(6) = 20 + 5\sin(\frac{\pi}{6} \times 6) = 20 + 5\sin(\pi) = 20 + 5 \times 0 = 20$$

Question 1

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

Accepted Answer

A function that can be written as $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$n is a $$non-negative integer and $$a_n, \ldots, a_0$ are real numbers.

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream by $$C(t) = 5t^2$ - 3t + 2$$, where $$t is $$time in hours. What is the concentration after 4 hours?

Accepted Answer

$$C(4) = 5(4)^2$ - 3(4) + 2 = 80 - 12 + 2 = 70$$

Question 3

Which of the following is NOT a property of exponents?

Accepted Answer

$$a^m + a^n = a$$^{m+n}$$

Question 4

A biologist is studying the population growth of bacteria, modeled by $$P(t) = 200 \cdot 1.5^t. $$What is the population after 3 hours?

Accepted Answer

$$P(3) = 200 \cdot 1.5^3$ = 200 \cdot 3.375 = 675$$

Question 5

Which of the following is the correct solution to the quadratic equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 6

A chemical reaction rate is modeled by $$R(x) = 4x^2$ - 7x + 3. $$What is the rate when $$x = -2$$?

Accepted Answer

$$R(-2) = 4(-2)^2$ - 7(-2) + 3 = 16 + 14 + 3 = 33$$

Question 7

Which of the following expressions is equivalent to $$\frac{2x^3$y^2$$}{$$4x^2y^5$}$$?

Accepted Answer

$$\frac{x}{2y^3$}$$

Question 8

A student is solving the equation $$2(x - 3) = 4x + 6. $$What is the value of $$x$$?

Accepted Answer

$$x = -6$$

Question 9

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 10

A medical researcher models the spread of a virus by $$V(t) = 100e$$^{0.2t}$$. What is the approximate value of V(5$$)$$? (Use e$$^{1}$$ \approx 2.718)$$

Accepted Answer

$$V(5) = 100e$$^{1}$$ \approx 100 	imes 2.718 = 271.8$$

Question 11

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

Accepted Answer

$$x = 5, y = 2$$

Question 12

A quadratic function models the height of a ball thrown upward: $$h(t) = -16t^2$ + 32t + 5. $$What is the maximum height reached by the ball?

Accepted Answer

The maximum occurs at $$t = -\frac{b}{2a} = -\frac{32}{2 	imes -16} = 1$$. $$h(1) = -16(1)^2$ + 32(1) + 5 = -16 + 32 + 5 = 21$$ feet.

Question 13

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$\sqrt{25 	imes 2} = 5\sqrt{2}$$

Question 14

A company’s profit is modeled by $$P(x) = -2x^2$ + 8x - 6$$, where $$x is $$the number of units sold. How many units should be sold to maximize profit?

Accepted Answer

$$x = 2$$

Question 15

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

Accepted Answer

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

Question 16

A hospital records the number of patients admitted each day as $$N(d) = 12d + 5. If 10 $$days have passed, how many patients have been admitted in total?

Accepted Answer

$$N(10) = 12 	imes 10 + 5 = 120 + 5 = 125$$

Question 17

Which of the following is the correct solution to $$\frac{2x - 4}{x + 3} = 0$$?

Accepted Answer

$$x = 2$$

Question 18

A scientist models the temperature of a reaction by $$T(t) = 20 + 5\sin(\frac{\pi}{6}t)$$, where $$t is $$time in minutes. What is the temperature at $$t = 6$$ minutes?

Accepted Answer

$$T(6) = 20 + 5\sin(\frac{\pi}{6} 	imes 6) = 20 + 5\sin(\pi) = 20 + 5 	imes 0 = 20$$

Question 19

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

Accepted Answer

$$x = -2$$

College Algebra: Course Syllabus and Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드