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

$$500 \times 2$$^{3}$$ = 4000$$

Question 1

Which of the following is the correct solution to the equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 2

A pharmaceutical company models the concentration $$C of a $$drug in the bloodstream over time $$t (in $$hours) by $$C(t) = 50e$$^{-0.2t}$$. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 50e$$^{-1}$$ \approx 18.4$$

Question 3

Which of the following represents the composition of functions $$f(x) = x^2$ and g(x) = x + 1$ as (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 4

A car rental company charges a base fee of $$\25$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 25 + 0.20m$$

Question 5

Given the quadratic equation $$x^2 - 6x + 8 = 0$, what are its solutions?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 6

Which of the following is the correct formula for the slope of a line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 7

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

Accepted Answer

$$500 	imes 2$$^{3}$$ = 4000$$

Question 8

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h}$$

Question 9

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (2, 1)$$

Question 10

Which of the following is the correct standard form of a linear equation?

Accepted Answer

$$Ax + By = C$$

Question 11

If $$f(x) = 3x - 2$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 2}{3}$$

Question 12

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1. $$What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 41$$ meters

Question 13

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$

Question 14

A matrix $$A is $$given by $$\begin{pmatrix} 2 & 3 \ 1 & 4 \end{pmatrix}. $$What is its determinant?

Accepted Answer

Question 15

Which of the following is the correct synthetic division result for dividing $$x^3$$ - $$6x^2 + 11x - 6$ by x - 1$?

Accepted Answer

$$x^2 - 5x + 6$

Question 16

Which of the following is the correct formula for the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Question 17

A medical test result is modeled by the absolute value equation $$|x - 5| = 3. $$What are the possible values of $$x$$?

Accepted Answer

$$x = 8$$ and $$x = 2$$

Question 18

Which of the following is the correct equation for a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x - h)^2$ + (y - k)^2$ = r^2$

Question 19

A company’s profit $$P is $$modeled by $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold. How many units should be sold to maximize profit?

Accepted Answer

$$x = 10$$

Comprehensive Study Notes for College Algebra: Equations, Functions, Graphs, and More

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