Question 1

A company tracks its profit using the function $$P(x) = 3x^2$ + 6x - 7$$, where $$x is $$the number of units sold (in thousands). What is the average rate of change of profit as sales increase from $$x to$$ $$x + h$$ units?

Accepted Answer

$$6x + 3h + 6$$

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream by $$C(t) = 25 - t$$, where $$t is $$the time in hours after administration. What is the difference quotient $$\frac{C(t+h) - C(t)}{h}$$, and what does it represent?

Accepted Answer

$$-1$$; it represents the constant rate at which the drug concentration decreases per hour.

Question 3

A business wants to find the equation of the line passing through the points $$(-10, 5)$$ and $$(-8, -3). $$What is the equation in slope-intercept form?

Accepted Answer

$$y = -4x - 35$$

Question 4

A company’s cost function is $$C(x) = x^2$ - 2x - 35$$, where $$x is $$the number of products produced. What is $$\lim_{x 	o 7} \frac{x^2$ - 2x - 35}{x - 7}$$?

Accepted Answer

$$12$$

Question 5

A chemical reaction’s rate is modeled by $$f(x) = \frac{x - 9}{x^2$ - 9x}. $$What is $$\lim_{x 	o 9} f(x)$$?

Accepted Answer

$$\frac{1}{9}$$

Question 6

A hospital monitors a patient’s temperature using $$T(x) = 6x + 11$$, where $$x is $$the number of hours after admission. What is $$\lim_{x 	o -5} T(x)$$?

Accepted Answer

$$-19$$

Question 7

A company’s revenue is given by $$R(x) = x(x - 2). $$What is $$\lim_{x 	o 5} R(x)$$?

Accepted Answer

$$15$$

Question 8

A function $$f(x) is $$defined as $$f(x) = \frac{(x + 5)^2$}{x^2$ - 25}. $$What is $$\lim_{x 	o -5} f(x)$$?

Accepted Answer

$$0$$

Question 9

A business’s profit function is $$P(x) = x^2$ - 2x - 35. $$What is $$\lim_{x 	o -5} P(x)$$?

Accepted Answer

$$0$$

Question 10

A function $$f(x) = \frac{x - 9}{x^2$ - 9x} is $$used to model a process. What is $$\lim_{x 	o 81} f(x)$$?

Accepted Answer

$$\frac{1}{81}$$

Question 11

A company’s cost function is $$C(x) = 3x + 6x^2$ - 7. $$What is $$C(x + h) - C(x)$$?

Accepted Answer

$$6hx + 3h + 6h^2$

Question 12

A function $$g(x) = x^2$ + 3x + 6$$ models the growth of a population. What is $$g(p + 3) in $$terms of $$p$$?

Accepted Answer

$$p^2 + 6p + 15$

Question 13

A function $$f(x) = \frac{x - 9}{x^2$ - 9x} is $$used in a business model. What is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$-\frac{1}{9}$$

Question 14

A function $$f(x) = \frac{(x + 5)^2$}{x^2$ - 25} is $$used to model depreciation. What is $$\lim_{x 	o 0} f(x)$$?

Accepted Answer

$$-1$$

Question 15

A quadratic equation $$9x^2 - 6x + 1 = 0$ models the break-even point for a product. What are the solutions for x$?

Accepted Answer

$$\frac{1}{3}$$

Question 16

A company’s profit is modeled by $$p^2 + 26p + 5 = 0$. What are the solutions for p$?

Accepted Answer

$$-5, -\frac{1}{5}$$

Question 17

A function $$f(x) = \frac{x^2$ - 5}{8 - x}$$ models the rate of a chemical reaction. What is $$\lim_{x 	o -8} f(x)$$?

Accepted Answer

$$\frac{59}{16}$$

Question 18

A function $$f(x) = 25 - x$$ models the temperature drop in a cooling process. What is $$f(x + h) - f(x)$$?

Accepted Answer

$$-h$$

Question 19

A function $$f(x) = 25 - x is $$used to model a process. What is the simplified difference quotient $$\frac{f(x + h) - f(x)}{h}$$?

Accepted Answer

$$-1$$

Question 20

A function $$f(x) = 3x + 4$$ models the cost of producing $$x$$ units. What is the $$y-$$intercept of this function, and what does it represent?

Accepted Answer

$$4$$; it represents the fixed cost when no units are produced.

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