Q: A hospital uses the function $$C(t) = 500e$$^{0.03t}$$ to model the cost of a treatment over time t$ (in months). What is the cost after 12 months?

$$C(12) = 500e$$^{0.36}$$ \approx 500 \times 1.433 \approx 716.5$$

Q: A chemical reaction is modeled by the exponential decay function $$N(t) = 1000e$$^{-0.05t}$$, where N$ is the amount of substance left after t$ hours. How much remains after 20 hours?

$$N(20) = 1000e$$^{-1}$$ \approx 1000 \times 0.368 \approx 368$$

Q: If $$A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$$, what is $$A + B$$?

$$\begin{pmatrix} 3 & 3 \\ 3 & 5 \end{pmatrix}$$

Q: Which of the following is the correct value for the determinant of the matrix $$\begin{pmatrix} 3 & 2 \\ 5 & 4 \end{pmatrix}$$?

$$3 \times 4 - 2 \times 5 = 12 - 10 = 2$$

Q: Which of the following is the correct sum for the geometric series $$2 + 6 + 18 + 54$$?

$$S = 2 \left( \frac{3^4$ - 1}{3 - 1} \right ) = 2 \left( \frac{81 - 1}{2} \right ) = 2 \times 40 = 80$$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

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

Accepted Answer

$$f(-2) = 19$$

Question 3

Which transformation occurs when the function $$f(x) is $$changed to $$f(x-4)$$?

Accepted Answer

The graph shifts 4 units right.

Question 4

A hospital uses the function $$C(t) = 500e$$^{0.03t}$$ to model the cost of a treatment over time t$ (in months). What is the cost after 12 months?

Accepted Answer

$$C(12) = 500e$$^{0.36}$$ \approx 500 	imes 1.433 \approx 716.5$$

Question 5

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

Accepted Answer

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

Question 6

Solve the quadratic equation $$x^2 - 5x + 6 = 0$.

Accepted Answer

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

Question 7

A chemical reaction is modeled by the exponential decay function $$N(t) = 1000e$$^{-0.05t}$$, where N$ is the amount of substance left after t$ hours. How much remains after 20 hours?

Accepted Answer

$$N(20) = 1000e$$^{-1}$$ \approx 1000 	imes 0.368 \approx 368$$

Question 8

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 9

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 10

Which of the following is the correct logarithmic form of the equation $$2^x = 16$$?

Accepted Answer

$$x = \log_2$ 16$$

Question 11

A business's revenue is modeled by $$R(x) = -2x^2$ + 40x$$, where $$x is $$the number of units sold. What number of units maximizes revenue?

Accepted Answer

$$x = 10$$

Question 12

Which of the following is the sum of the first 5 terms of the arithmetic sequence with $$a_1 = 3$ and d = 4$?

Accepted Answer

$$S_5 = 55$

Question 13

If $$A = \begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \ 2 & 1 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{pmatrix} 3 & 3 \ 3 & 5 \end{pmatrix}$$

Question 14

Which of the following is the correct solution to the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 15

A population grows according to $$P(t) = 2000 \cdot 1.05^t. $$What is the population after 8 years?

Accepted Answer

$$P(8) = 2000 \cdot 1.05^8$ \approx 2000 \cdot 1.477 \approx 2954$$

Question 16

Which of the following is the correct value for the determinant of the matrix $$\begin{pmatrix} 3 & 2 \ 5 & 4 \end{pmatrix}$$?

Accepted Answer

$$3 	imes 4 - 2 	imes 5 = 12 - 10 = 2$$

Question 17

Which of the following is the correct sum for the geometric series $$2 + 6 + 18 + 54$$?

Accepted Answer

$$S = 2 \left( \frac{3^4$ - 1}{3 - 1} ight ) = 2 \left( \frac{81 - 1}{2} ight ) = 2 	imes 40 = 80$$

Question 18

Which of the following is the correct property of logarithms for $$\log_b (xy)$$?

Accepted Answer

$$\log_b (xy) = \log_b x + \log_b y$$

College Algebra Syllabus and Course Structure Overview

Guida di studio - Domande di pratica

Study guide - Flashcard