Question 1

Which of the following is the correct solution to the inequality $$2x - 5 \u003e 9$$?

Accepted Answer

$$x \u003e 7$$

Question 2

A chemical reaction requires the temperature $$T (in $$degrees Celsius) to satisfy $$T^2 - 4T - 5$$ \u003c 0$$. What is the range of acceptable temperatures?

Accepted Answer

$$-1 \u003c T \u003c 5$$

Question 3

Which of the following is the inverse function of $$f(x) = 3x + 2$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 2}{3}$$

Question 4

A population of bacteria doubles every hour. If the initial population is $$P_0$$, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2^t$$

Question 5

Solve for $$x$$: $$\log_{2}(x) = 5$$

Accepted Answer

$$x = 32$$

Question 6

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$x = 3$$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

$$V(3) = 20000 \cdot (0.85)^3$ \approx 12251$$

Question 10

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 11

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 12

A medical test result is modeled by the function $$f(x) = x^2$ - 8x + 15. $$For which value of $$x$$ does the result reach its minimum?

Accepted Answer

$$x = 4$$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

$$x = 6$$

Question 15

A company’s profit $$P is $$modeled by $$P(x) = -2x^2$ + 8x - 6$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$P_{max} = 2$$

Question 16

Which of the following is the correct solution to the exponential equation $$5^{x} = 125$?

Accepted Answer

$$x = 3$$

Question 17

A circle has the equation $$x^2$$ + $$y^2 = 49$. What is the radius of the circle?

Accepted Answer

$$7$$

Question 18

Which of the following is the correct solution to the polynomial equation $$x^3 - 8 = 0$?

Accepted Answer

$$x = 2$$

Question 19

A radioactive substance decays according to $$A(t) = 100e$$^{-0.3t}$$. How long will it take for the substance to decay to 50$ units?

Accepted Answer

$$t \approx 2.31$$

Question 20

Which of the following is the correct solution to the equation $$\sqrt{x + 9} = 5$$?

Accepted Answer

$$x = 16$$

College Algebra with Lab Syllabus and Course Policies

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