Question 1

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

Accepted Answer

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

Question 2

A biologist models the population of bacteria with the exponential function $$P(t) = 500e$$^{0.2t}$$. What is the population after 5 hours?

Accepted Answer

$$P(5) = 500e$$^{1}$$ \approx 1359.14$$

Question 3

Which of the following is the vertex of the quadratic function $$f(x) = 2x^2$ - 8x + 3$$?

Accepted Answer

$$(2, -5)$$

Question 4

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -3x^2$ + 24x + 60$$, where $$x is $$the number of items sold (in thousands). What is the maximum revenue?

Accepted Answer

$$R(4) = 108$$ thousand dollars

Question 5

Which of the following is the correct solution to $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 6

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

Accepted Answer

$$x = 2$$, $$y = 1$$

Question 7

Which of the following is the correct equation for the line of best fit given points $$(1, 2)$$, $$(2, 4)$$, and $$(3, 6)$$?

Accepted Answer

$$y = 2x$$

Question 8

A radioactive substance decays according to $$A(t) = 100e$$^{-0.3t}$$. How much remains after 10 hours?

Accepted Answer

$$A(10) = 100e$$^{-3}$$ \approx 4.98$$

Question 9

Which of the following is the correct solution to $$\sqrt{x + 4} = 5$$?

Accepted Answer

$$x = 21$$

Question 10

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$h(2.04) \approx 21.9$$ meters

Question 11

Which of the following is the correct solution to the logarithmic equation $$\log_{2}(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 12

A scientist uses the regression equation $$y = 0.8x + 2 to $$predict the concentration of a chemical. What is the predicted concentration when $$x = 10$$?

Accepted Answer

$$y = 10$$

Question 13

Which of the following is the correct solution to the equation $$x^2 = 49$?

Accepted Answer

$$x = 7 or$$ $$x = -7$$

Question 14

Given the matrix equation $$\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}$$, what is the value of $$x$$?

Accepted Answer

$$x = 1$$

Question 15

Which of the following is the correct solution to the radical equation $$\sqrt{2x - 1} = 3$$?

Accepted Answer

$$x = 5$$

Question 16

A population grows according to $$P(t) = 200e$$^{0.05t}$$. How long will it take for the population to double?

Accepted Answer

$$t \approx 13.86$$ years

Question 17

Which of the following is the correct solution to the equation $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 18

A quadratic equation $$ax^2 + bx + c = 0$ has complex roots. Which condition must be true?

Accepted Answer

$$b^2 - 4ac$$ \u003c 0$$

Question 19

Which of the following is the correct solution to the system $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3$$, $$y = 2$$

Question 20

Which of the following is the correct solution to the equation $$e^{x} = 7$?

Accepted Answer

$$x = \ln 7$$

College Algebra I: Final Exam Review (Chapters 1, 6, 12)

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