Q: A hospital uses the formula $$P = 1200e$$^{0.03t}$$ to model the number of bacteria present after t$ hours. What is the approximate number of bacteria after 10 hours? (Round to the nearest whole number)

$$P = 1200e$$^{0.3}$$ \approx 1200 \times 1.3499 \approx 1620$$

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

$$V = 20000(0.85)^3$ = 20000 \times 0.614125 = 12282.50$$

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 
eq 0$.

Question 2

A chemical reaction is modeled by the equation $$C(t) = 5t^2$ - 3t + 2$$, where $$C is $$the concentration in mol/L and $$t is $$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 the solution set for the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7$$ and $$x = -2$$

Question 4

A hospital uses the formula $$P = 1200e$$^{0.03t}$$ to model the number of bacteria present after t$ hours. What is the approximate number of bacteria after 10 hours? (Round to the nearest whole number)

Accepted Answer

$$P = 1200e$$^{0.3}$$ \approx 1200 	imes 1.3499 \approx 1620$$

Question 5

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 6

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, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$P(3) = -2(3)^2$ + 12(3) - 16 = -18 + 36 - 16 = 2$$ thousand dollars, at $$x = 3$$ thousand units.

Question 7

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

All real numbers except $$x = 3$$ and $$x = -3$$

Question 8

Solve the inequality $$3x - 7 \u003c 2x + 5.$$

Accepted Answer

$$x \u003c 12$$

Question 9

A population of bacteria doubles every 5 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 	imes 2$$^{t/5}$$

Question 10

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 11

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

Accepted Answer

$$V = 20000(0.85)^3$ = 20000 	imes 0.614125 = 12282.50$$

Question 12

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

Accepted Answer

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

Question 13

A student is analyzing the function $$f(x) = \sqrt{x - 3}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 3$$

Question 14

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

Accepted Answer

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

Question 15

A biologist models the growth of a plant with $$h(t) = 2t^2$ + 5t + 3$$, where $$h is $$the height in cm and $$t is $$time in weeks. What is the height after 6 weeks?

Accepted Answer

$$h(6) = 2(6)^2$ + 5(6) + 3 = 72 + 30 + 3 = 105 cm$$

Question 16

Which of the following is the correct solution to the equation $$2^{x} = 64$?

Accepted Answer

$$x = 6$$

Question 17

A student is asked to solve the rational equation $$\frac{x}{x-2} = 3. $$What is the solution?

Accepted Answer

$$x = 6$$

Question 18

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

Accepted Answer

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

Question 19

A student is analyzing the graph of $$y = -x^2$ + 4x - 3. $$What is the vertex of the parabola?

Accepted Answer

$$(2, 1)$$

College Algebra Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard