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: 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?

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

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 $0 < b < 1$

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

Study Guide - Practice Questions

Study Guide - Flashcards