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

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

Question 1

A pharmaceutical company models the concentration of a drug in the bloodstream over time with the function $$C(t) = 5e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 3 hours?

Accepted Answer

$$C(3) = 5e$$^{-0.6}$$ \approx 2.74$$

Question 2

Which of the following is the correct formula for the midpoint between the points $$(2, 5)$$ and $$(8, -3)$$?

Accepted Answer

$$(5, 1)$$

Question 3

A company’s profit $$P(x) in $$thousands of dollars is modeled by the quadratic function $$P(x) = -2x^2$ + 12x - 16$$, 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 $$P(3) = 2$$ thousand dollars at $$x = 3$$ thousand units.

Question 4

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

Accepted Answer

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

Question 5

A circle has its center at $$(4, -2)$$ and passes through the point $$(7, 2). $$What is the equation of the circle?

Accepted Answer

$$(x - 4)^2$ + (y + 2)^2$ = 25$$

Question 6

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 7

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

Accepted Answer

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

Question 8

Which of the following is the correct solution to the inequality $$\frac{2x - 3}{x + 1} \u003e 1$$?

Accepted Answer

$$x \u003e 4 or$$ $$x \u003c -1$$

Question 9

Which of the following is the correct logarithmic form of the exponential equation $$7^x = 20$$?

Accepted Answer

$$x = \log_7$ 20$$

Question 10

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

Accepted Answer

Maximum height is $$h(2.04) \approx 22.4$$ meters.

Question 11

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

All real numbers except $$x = 3$$ and $$x = -3$$

Question 12

If $$f(x) = \log_2$(x)$$, what is $$f(8)$$?

Accepted Answer

$$f(8) = 3$$

Question 13

A rational function $$R(x) = \frac{x^2$ - 4}{x - 2} is $$simplified for $$x 
eq 2. $$What is the simplified form?

Accepted Answer

$$R(x) = x + 2$$

Question 14

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

Accepted Answer

$$x = -1$$ and $$x = -5$$

Question 15

A car’s value depreciates exponentially according to $$V(t) = 20000e$$^{-0.15t}$$, where t$ is years after purchase. What is the value after 5 years?

Accepted Answer

$$V(5) = 20000e$$^{-0.75}$$ \approx 9440$$

Question 16

Which of the following is the correct equation for a line passing through $$(1, 2)$$ with slope $$-3$$?

Accepted Answer

$$y - 2 = -3(x - 1)$$

Question 17

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

Accepted Answer

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

Question 18

A quadratic equation $$x^2 - 4x + 4 = 0$ has which type of roots?

Accepted Answer

One real repeated root

Question 19

Which of the following is the correct solution for $$\log_5$(x) = 2$$?

Accepted Answer

$$x = 25$$

Question 20

A rational inequality $$\frac{x + 2}{x - 1} \u003c 0 is $$satisfied for which values of $$x$$?

Accepted Answer

$$-2 \u003c x \u003c 1$$

Precalculus Study Guide: Functions, Graphs, and Polynomial/Rational Functions

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