Question 1

A chemical reaction is modeled by the equation $$2x + 5 = 17. $$What is the value of $$x$$ representing the amount of reactant needed for the reaction to reach completion?

Accepted Answer

$$x = 6$$

Question 2

A biologist measures the population growth using the exponential function $$P(t) = 500e$$^{0.03t}$$. What is the population after 10 years, rounded to the nearest whole number?

Accepted Answer

$$P(10) \approx 677$$

Question 3

A circle is used to model the cross-section of a pipe. If the equation of the circle is $$(x-3)^2$$ + $$(y+2)^2 = 16$, what is the center and radius of the pipe?

Accepted Answer

Center $$(3, -2)$$, radius $$4$$

Question 4

A pharmaceutical company needs to solve the quadratic equation $$x^2 - 6x + 8 = 0$ to determine the concentration of a drug. What are the possible concentrations?

Accepted Answer

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

Question 5

A medical device uses the function $$f(x) = \frac{1}{x-2} to $$calculate dosage. What is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 6

A financial analyst models profit with $$y = mx + b. If $$the profit increases by $$5$$ units for every $$1$$ unit increase in sales, and the initial profit is $$20$$, what is the equation of the line?

Accepted Answer

$$y = 5x + 20$$

Question 7

A scientist is analyzing the function $$g(x) = \sqrt{x-4}. $$What is the domain of $$g(x)$$?

Accepted Answer

$$x \geq 4$$

Question 8

A researcher uses the quadratic formula to solve $$2x^2 + 3x - 2 = 0$. What are the solutions?

Accepted Answer

$$x = \frac{1}{2}$$ and $$x = -2$$

Question 9

A population model uses the function $$f(x) = x^3$ - 4x. $$How many turning points does the graph of $$f(x)$$ have?

Accepted Answer

2

Question 10

A physicist analyzes the rational function $$h(x) = \frac{x^2$ - 9}{x^2$ - 4x + 3}. $$What are the vertical asymptotes of $$h(x)$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 11

A medical test result is modeled by $$|x - 5| \u003c 3. $$What is the range of possible values for $$x$$?

Accepted Answer

$$2 \u003c x \u003c 8$$

Question 12

A chemical solution is modeled by the equation $$\frac{2}{x} = 4. $$What is the value of $$x$$?

Accepted Answer

Question 13

A patient’s heart rate is modeled by $$f(x) = 3x + 7. If $$the input $$x is $$doubled, what is the new function?

Accepted Answer

$$f(2x) = 3(2x) + 7 = 6x + 7$$

Question 14

A scientist uses the function $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(3) = 9$$

Question 15

A researcher is analyzing the function $$f(x) = \frac{1}{x^2$ - 4}. $$What values must be excluded from the domain?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 16

A physicist models radioactive decay with $$y = 100e$$^{-0.05t}$$. What is the value of y$ after 20$ units of time?

Accepted Answer

$$y \approx 36.79$$

Question 17

A business uses the logarithmic function $$y = \log_{10}(x) to $$model sales growth. If sales reach $$x = 1000$$, what is the value of $$y$$?

Accepted Answer

$$y = 3$$

Question 18

A medical researcher solves the equation $$x^2 + 4 = 0$ to find possible values for a measurement. What are the solutions?

Accepted Answer

$$x = 2i$$ and $$x = -2i$$

Question 19

A scientist is analyzing the function $$f(x) = x^4$ - 2x^2$ + 1. $$What is the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

College Algebra Study Guide: Equations, Coordinate Systems, Functions, and More

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