Question 1

A pharmaceutical company is testing a new drug. The concentration of the drug in the bloodstream after $$t$$ hours is modeled by $$C(t) = 50e$$^{-0.2t}$$. What is the concentration after 5 hours, rounded to the nearest whole number?

Accepted Answer

$$18$$

Question 2

Which of the following is the solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 3

A biologist is tracking the population of bacteria, which doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$4000$$

Question 4

Which of the following is the correct definition of a function?

Accepted Answer

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

Question 5

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 $$20 at$$ $$x = 3$$

Question 6

Which of the following is the solution to the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 7

A chemical reaction follows the equation $$y = 5x^2$ - 3x + 2. If$$ $$x = 4$$, what is the value of $$y$$?

Accepted Answer

$$74$$

Question 8

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

Accepted Answer

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

Question 9

A student is analyzing the quadratic equation $$x^2 - 6x + 8 = 0$. What are the solutions?

Accepted Answer

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

Question 10

Which of the following is the correct formula for exponential decay?

Accepted Answer

$$y = y_0$ e$$^{-kt}$$

Question 11

A city’s population is modeled by $$P(t) = 12000(1.03)^t$$, where $$t is $$the number of years since 2020. What will the population be in 5 years?

Accepted Answer

$$13907$$

Question 12

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 13

Which of the following is the correct property of logarithms?

Accepted Answer

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

Question 14

A piecewise function is defined as $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

$$9$$

Question 15

Which of the following is the correct formula for the midpoint between points $$(2, 5)$$ and $$(8, 9)$$?

Accepted Answer

$$(5, 7)$$

Question 16

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-0.05t}$$. If the initial amount is 100$ grams, how much remains after 20$ years?

Accepted Answer

$$36.8$$ grams

Question 17

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

Accepted Answer

$$x = 32$$

Question 18

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

Accepted Answer

$$22$$ meters

Question 19

Which of the following is the correct formula for the distance between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 20

Which of the following is the correct solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

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