Question 1

A biologist is studying the population of bacteria in a petri dish. The population doubles every 3 hours. If the initial population is 200, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 200 \cdot 2^{t/3}$

Question 2

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

Accepted Answer

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

Question 3

A ladder 10 feet long leans against a wall. The bottom of the ladder is 6 feet from the wall. How high up the wall does the ladder reach?

Accepted Answer

$8$ feet

Question 4

Suppose the function $f(x) = x^2 - 4x + 3$. What is the average rate of change of $f$ on the interval $[1, 5]$?

Accepted Answer

$-2$

Question 5

A Ferris wheel has a radius of 20 feet and rotates once every 40 seconds. If a rider starts at the lowest point, which function models the height $h$ (in feet) above the ground after $t$ seconds?

Accepted Answer

$h(t) = 20 \sin\left(\frac{\pi t}{20}\right) + 20$

Question 6

If $\log_2(x) = 5$, what is the value of $x$?

Accepted Answer

$32$

Question 7

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Accepted Answer

$13$

Question 8

Which of the following is equivalent to $\sin^2(x) + \cos^2(x)$?

Accepted Answer

$1$

Question 9

A population of deer in a park is modeled by $P(t) = 500e^{0.04t}$, where $t$ is in years. What is the population after 5 years?

Question 10

If $f(x) = 2x + 1$ and $g(x) = x^2$, what is $(f \circ g)(3)$?

Accepted Answer

$19$

Question 11

A ball is thrown upward from the ground with an initial velocity of 32 ft/s. Its height after $t$ seconds is given by $h(t) = 32t - 16t^2$. What is the maximum height reached by the ball?

Accepted Answer

$16$ ft

Question 12

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

Accepted Answer

$x = 4$

Question 13

Suppose $f(x) = \sqrt{x-1}$. What is the domain of $f$?

Accepted Answer

$[1, \infty)$

Question 14

A chemical reaction decays according to $C(t) = 100e^{-0.2t}$, where $C$ is the concentration in mg/L and $t$ is in hours. What is the concentration after 10 hours?

Accepted Answer

$13.53$ mg/L

Question 15

If $	an(	heta) = \frac{3}{4}$ and $	heta$ is in Quadrant I, what is $\sin(	heta)$?

Accepted Answer

$\frac{3}{5}$

Question 16

Which of the following is equivalent to $\log_3(27)$?

Accepted Answer

$3$

Question 17

A car depreciates in value by 15% each year. If the initial value is $20,000, what is the value after 3 years?

Accepted Answer

$12,282.50$

Question 18

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

Accepted Answer

$3$

Question 19

A right triangle has an angle $	heta$ such that $\sin(	heta) = 0.6$. What is $\cos(	heta)$ if $	heta$ is in Quadrant I?

Accepted Answer

$0.8$

Question 20

Which of the following is the solution to $\log_{10}(x) = 2$?

Accepted Answer

$100$

Precalculus Final Exam Review: Key Concepts and Applications

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