Question 1

Which of the following equations represents the equation of a line in slope-intercept form that passes through the point $$(2, 5)$$ and has a slope of $$-3$$?

Accepted Answer

$$y = -3x + 11$$

Question 2

A pharmaceutical company models the decay of a drug in the bloodstream by the function $$C(t) = 50e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5$ hours?

Accepted Answer

$$C(5) = 50e$$^{-1}$$ \approx 18.4 mg/L$$

Question 3

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 4

A business invests $$\10$$,000$$ in an account that earns 6$$\%$$ annual interest compounded monthly. What will the balance be after 3$ years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$A = 10000(1 + \frac{0.06}{12}$$)^{36}$$ \approx \11$$,972$

Question 5

Which of the following is the correct factorization of the quadratic $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 6

A chemical reaction follows the equation $$A = A_0e$$^{-kt}$$, where A_0$ is the initial amount, k$ is a positive constant, and t$ is time. If A_0$ = 100$$ grams, $$k = 0.1$$, and $$t = 20$$ minutes, what is the remaining amount of substance?

Accepted Answer

$$A = 100e$$^{-2}$$ \approx 13.5$$ grams

Question 7

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

Accepted Answer

$$x = 2, y = 1$$

Question 8

Which of the following expressions is equivalent to $$\log_{2} 32$$?

Accepted Answer

$$5$$

Question 9

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 $$P(3) = 2$$ thousand dollars, at $$x = 3$$ thousand units

Question 10

Which of the following is the correct solution to the equation $$\frac{3}{x} + 2 = 5$$?

Accepted Answer

$$x = 1$$

Question 11

A patient is prescribed a medication that is administered every $$8$$ hours. The amount of medication in the bloodstream is modeled by $$A(t) = 100(0.5$$)^{t/8}$$, where t$ is in hours. What is the amount of medication just before the next dose?

Accepted Answer

$$A(8) = 100(0.5$$)^{1}$$ = 50 mg$$

Question 12

Which of the following is the correct solution to the equation $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 13

A matrix $$A is $$given by $$A = \begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}. $$What is the determinant of $$A$$?

Accepted Answer

$$5$$

Question 14

Which of the following is the correct solution to the quadratic equation $$x^2 + 4x + 1 = 0$?

Accepted Answer

$$x = -2 \pm \sqrt{3}$$

Question 15

A car depreciates in value according to the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after $$4$$ years?

Accepted Answer

$$V(4) = 20000(0.85)^4$ \approx \10441$

Question 16

Which of the following is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 17

A student is planning to take out a loan of $$\5$$,000$$ at an annual interest rate of 4$$\%$$ compounded quarterly. What will be the amount owed after 2$ years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$)

Accepted Answer

$$A = 5000(1 + \frac{0.04}{4}$$)^{8}$$ \approx \5$$,412$

Question 18

Which of the following is the solution to the equation $$\log_{10}(x) = 2$$?

Accepted Answer

$$x = 100$$

Question 19

A company has two investment options: Option A pays $$5\%$$ simple interest per year, and Option B pays $$4.8\%$$ compounded annually. If you invest $$\1$$,000$$ for 5$ years, which option yields a higher return and by how much?

Accepted Answer

Option B yields more: $$A = 1000(1.048)^5$ \approx \1$$,265$$ vs. Option A: A = 1000 + 1000$$ 	imes 0.05 	imes 5 = \$$1,250$$; difference is $$\15$

College Algebra Syllabus and Course Overview – Fall 2023

Guida di studio - Domande di pratica

Study guide - Flashcard