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

$$C(5) = 50e$$^{-0.2 \times 5}$$ = 50e$$^{-1}$$ \approx 18.4 mg/L$$

Question 1

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

Accepted Answer

$$C(5) = 50e$$^{-0.2 	imes 5}$$ = 50e$$^{-1}$$ \approx 18.4 mg/L$$

Question 2

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

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3$$

Question 3

A population of bacteria doubles every 4 hours. If the initial population is 500, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/4}$$

Question 4

Solve the quadratic equation $$x^2 - 6x + 8 = 0$.

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Question 5

Which of the following describes the transformation applied to $$f(x) = x^2$ to obtain g(x$$) = $$(x-3)^2 + 5$?

Accepted Answer

Shift right by 3 units and up by 5 units

Question 6

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = 2x^2$ + 1$$

Question 7

A chemical reaction follows the equation $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount of reactant remaining after t$ minutes. How long will it take for only 40 units of reactant to remain?

Accepted Answer

$$t = -\frac{1}{0.05} \ln\left(\frac{40}{100}\right) \approx 18.33$$ minutes

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

Solve the absolute value equation $$|2x - 5| = 7.$$

Accepted Answer

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

Question 10

A business's revenue is modeled by $$R(x) = -2x^2$ + 40x + 100$$, where $$x is $$the number of units sold. What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$R(10) = 300 at$$ $$x = 10$$ units

Question 11

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}$$?

Accepted Answer

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

Question 12

Which of the following is the correct range for the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$f(x) \geq 0$$

Question 13

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

Vertex at $$(2, 3)$$

Question 14

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

Accepted Answer

$$x = 32$$

Question 15

A rational function is given by $$f(x) = \frac{x^2$ - 9}{x - 3}. $$What is the simplified form for $$x 
eq 3$$?

Accepted Answer

$$f(x) = x + 3$$

Question 16

A medical test result is modeled by $$T(x) = 5 \ln(x)$$, where $$x is $$the concentration of a substance. If $$T(x) = 10$$, what is the concentration $$x$$?

Accepted Answer

$$x = e$$^{2}$$

Question 17

Which of the following is the solution to the system of equations: $$\begin{cases} x + y + z = 6 \ 2x - y + z = 7 \ x - 2y + 3z = 8 \end{cases}$$?

Accepted Answer

$$x = 2$$, $$y = 1$$, $$z = 3$$

Question 18

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h}$$

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