Question 1

A manufacturer wants to maximize profit by producing two products, A and B. The profit function is given by $P(x, y) = 5x + 4y - 0.5x^2 - 0.25y^2$, where $x$ and $y$ are the number of units produced of A and B, respectively. What is the maximum profit, and how many units of each product should be produced?

Accepted Answer

Maximum profit is $32$ at $x = 5$, $y = 8$

Question 2

Given the quadratic function $f(x) = -2x^2 + 8x + 10$, what is the maximum value of $f(x)$ and at what value of $x$ does it occur?

Accepted Answer

Maximum value is $18$ at $x = 2$

Question 3

A company invests $P$ dollars at an annual interest rate of $r$ compounded annually. The amount after $t$ years is given by $A = P(1 + r)^t$. If $P = 1000$, $r = 0.05$, and $t = 3$, what is the final amount?

Accepted Answer

$A = 1157.63$

Question 4

Which of the following is the correct factorization of $x^2 - 5x + 6$?

Accepted Answer

$(x - 2)(x - 3)$

Question 5

If $f(x) = 2x^2 - 3x + 1$, what is $f(4)$?

Accepted Answer

$f(4) = 21$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is $500$, what will the population be after $9$ hours?

Accepted Answer

$4000$

Question 7

Solve for $x$: $2x + 5 = 17$

Accepted Answer

$x = 6$

Question 8

Which of the following is the solution set for the inequality $x^2 - 4 < 0$?

Accepted Answer

$-2 < x < 2$

Question 9

A car depreciates in value according to the function $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value of the car after $5$ years?

Accepted Answer

$V(5) = 8860.6$

Question 10

Which of the following is the vertex of the parabola $y = x^2 - 6x + 8$?

Accepted Answer

$(3, -1)$

Question 11

If $g(x) = x^3 - 2x^2 + x - 5$, what is $g(-2)$?

Accepted Answer

$g(-2) = -27$

Question 12

Which of the following is the correct solution to the equation $x^2 + 4x + 4 = 0$?

Accepted Answer

$x = -2$

Question 13

A student invests $1500$ in an account that earns $6\%$ annual interest compounded monthly. What is the value of the investment after $2$ years? Use $A = P(1 + \frac{r}{n})^{nt}$.

Accepted Answer

$A = 1696.89$

Question 14

Which of the following is the correct solution to the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 3$, $y = 1$

Question 15

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

Accepted Answer

$x 
eq 3$

Question 16

A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter is 36 meters, what are the dimensions of the garden?

Accepted Answer

Width = $5$ m, Length = $13$ m

Question 17

Which of the following is the correct solution to $|2x - 5| = 7$?

Accepted Answer

$x = 6$, $x = -1$

Question 18

If $h(x) = \sqrt{x + 4}$, what is the range of $h(x)$?

Accepted Answer

$h(x) \geq 0$

Question 19

A chemical reaction's rate is modeled by $R(t) = 100e^{-0.2t}$, where $t$ is time in minutes. What is the rate after $10$ minutes?

Accepted Answer

$R(10) = 13.53$

Question 20

Which of the following is the correct solution to the equation $3x^2 - 12 = 0$?

Accepted Answer

$x = 2$, $x = -2$

College Algebra Study Notes: Sequences, Series, and Financial Applications

Study Guide - Practice Questions

Study Guide - Flashcards