Q: A population of bacteria triples every 2 hours. If the initial population is 100, what is the population after 6 hours?

$$100 \times 3$$^{3}$$ = 100 \times 27 = 2700$$

Q: If $$f(x) = 4x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

$$f(g(2)) = f(4) = 4 \times 4 - 7 = 16 - 7 = 9$$

Question 1

A car's value depreciates from $$\20$$,000$$ to $$\$$15,000$$ over 3 years. What is the average rate of change of the car's value per year?

Accepted Answer

$$\1$$,667$ per year

Question 2

Given the function $$f(x) = 3x + 2$$, what is the slope and what does it represent in a real-world context where $$x is $$hours worked and $$f(x) is $$total pay?

Accepted Answer

Slope is $$3$$, representing pay per hour.

Question 3

If $$A = P(1 + r/n$$)^{nt}$$, what is the accumulated amount after 5 years if P = 1000$, r = 0.04$, n = 2$ (compounded semiannually)?

Accepted Answer

$$A = 1000(1 + 0.02$$)^{10}$$ = 1000(1.219)$$, so $$A \approx \1219$

Question 4

Which of the following is the correct formula for continuous compound interest?

Accepted Answer

$$A = Pe$$^{rt}$$

Question 5

A savings plan uses the formula $$F = P(1 + r)^n. If $$you deposit $$\500$ at 5$$\%$ annual interest compounded yearly for 4 years, what is the future value?

Accepted Answer

$$F = 500(1 + 0.05)^4$ = 500(1.2155) \approx \607.75$

Question 6

Given the data set: $$2, 4, 4, 6, 8$$, what is the mean?

Accepted Answer

$$\frac{2 + 4 + 4 + 6 + 8}{5} = \frac{24}{5} = 4.8$$

Question 7

A company’s revenue function is $$R(x) = 50x$$, and its cost function is $$C(x) = 30x + 200. $$What is the break-even point?

Accepted Answer

$$x = 10$$

Question 8

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

Accepted Answer

All real numbers except $$x = 3$$

Question 9

If $$f(x) = 2x^2$ - 3x + 1$$, evaluate $$f(-2).$$

Accepted Answer

$$2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15$

Question 10

A population of bacteria triples every 2 hours. If the initial population is 100, what is the population after 6 hours?

Accepted Answer

$$100 	imes 3$$^{3}$$ = 100 	imes 27 = 2700$$

Question 11

Which of the following is the correct equation for an exponential decay function?

Accepted Answer

$$y = a \cdot b$$^{x}$$, where 0$$ \u003c b \u003c 1$$

Question 12

If you roll two six-sided dice, how many possible outcomes are there?

Accepted Answer

$$36$$

Question 13

A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Accepted Answer

$$\frac{3}{10}$$

Question 14

Given points $$(2, 5)$$ and $$(6, 13)$$, what is the equation of the line passing through them?

Accepted Answer

$$y = 2x + 1$$

Question 15

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.2$$

Question 16

Which of the following best describes the range of the function $$f(x) = x^2$ + 3$$?

Accepted Answer

$$[3, \infty)$$

Question 17

A loan of $$\2000$ is to be paid back in 3 years at an annual interest rate of 6$$\%$ compounded annually. What is the total amount owed at the end of 3 years?

Accepted Answer

$$2000(1 + 0.06)^3$ = 2000(1.191016) \approx \2382.03$

Question 18

If $$f(x) = 4x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(4) = 4 	imes 4 - 7 = 16 - 7 = 9$$

Question 19

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-0.2t}$$. If N_0$ = 100$$, what is $$N(5)$$?

Accepted Answer

$$100e^{-1}$$ \approx 36.79$$

Question 20

If the probability of rain on any given day is $$0.3$$, what is the probability that it does not rain?

Accepted Answer

$$0.7$$

Math 119 Final Exam Concept List: College Algebra Study Guide

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