Question 1

A pharmaceutical company models the concentration of a drug in a patient's bloodstream over time with the quadratic function $$C(t) = -0.5t^2$ + 4t$$, where $$C is $$concentration in mg/L and $$t is $$time in hours. What is the maximum concentration, and at what time does it occur?

Accepted Answer

Maximum concentration is $$8 mg/L at$$ $$t = 4$$ hours.

Question 2

A company wants to fit a linear model to predict sales based on advertising spending. If the data points are $$(2, 5)$$, $$(4, 9)$$, and $$(6, 13)$$, what is the equation of the best-fit line?

Accepted Answer

$$y = 2x + 1$$

Question 3

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 4

A hospital uses the function $$f(x) = 3x + 2 to $$estimate the number of staff needed based on the number of patients $$x. If $$there are $$20$$ patients, how many staff are needed?

Accepted Answer

$$62$$

Question 5

Which of the following graphs represents a quadratic function?

Accepted Answer

A parabola opening upward or downward.

Question 6

A piecewise-defined function is used to model a tax rate: $$T(x) = \begin{cases} 0.1x & x \leq 10000 \ 0.2x & x \u003e 10000 \end{cases}. $$What is the tax for an income of $$12000$$?

Accepted Answer

$$2400$$

Question 7

A student is analyzing the function $$f(x) = |x - 3|. $$Which statement is true about its graph?

Accepted Answer

It has a vertex at $$(3, 0)$$ and is V-shaped.

Question 8

A chemical reaction is modeled by the power function $$y = kx^n. If $$doubling $$x$$ quadruples $$y$$, what is the value of $$n$$?

Accepted Answer

$$n = 2$$

Question 9

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 3)$$

Question 10

A business wants to maximize profit modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units should be sold?

Accepted Answer

Maximum profit is $$16 at$$ $$x = 3$$

Question 11

Which of the following is the correct equation for a line passing through $$(1, 2)$$ with slope $$3$$?

Accepted Answer

$$y = 3x - 1$$

Question 12

A quadratic equation $$x^2 - 6x + 9 = 0$ models the height of a projectile. What are the solutions for x$?

Accepted Answer

$$x = 3$$

Question 13

A city models population growth with the function $$P(t) = 5000(1.02)^t$$, where $$t is $$years. What is the population after $$5$$ years?

Accepted Answer

$$5520$$

Question 14

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 15

A student is asked to solve the inequality $$2x - 5 \u003c 7. $$What is the solution?

Accepted Answer

$$x \u003c 6$$

Question 16

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(h, k). $$What is the formula for $$h$$?

Accepted Answer

$$h = -\frac{b}{2a}$$

Question 17

A scientist uses the function $$y = \sqrt{x} to $$model the rate of a reaction. What is the value of $$y$$ when $$x = 16$$?

Accepted Answer

$$4$$

Question 18

Which of the following is the solution to the equation $$|x - 4| = 6$$?

Accepted Answer

$$x = 10 or$$ $$x = -2$$

Question 19

A business models revenue with $$R(x) = 5x^3$ - 2x^2$ + x$$, where $$x is $$the number of products sold. What is the degree of this polynomial?

Accepted Answer

$$3$$

Question 20

A student is given the function $$f(x) = 2x^2$ - 8x + 6. $$What is the minimum value of $$f(x)$$?

Accepted Answer

$$-2$$

College Algebra: Polynomials and Functions – Syllabus and Study Guide (MAT 112A)

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