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?

Accepted Answer

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

Guida di studio - Domande di pratica

Study guide - Flashcard