Q: Find the average cost per board for the company in the previous question if $$x = 30$$ boards are produced per day.

$$\frac{C(30)}{30} = \frac{300 + 24 \times 30}{30} = 34$$

Q: Suppose $$2,500 is $$invested at $$7 ext{\%}$$ compounded quarterly. How much money will be in the account after $$15$$ years?

$$A = 2,500 \times (1 + 0.07/4$$)^{60}$$ \approx 7,200$$

Question 1

A company models the price-demand relationship for microchips with the function $$p(x) = 75 - 3x$$, where $$p is $$the price per chip in dollars and $$x is $$the number of chips sold in millions. What is the price per chip if the company sells 7 million chips?

Accepted Answer

$$p(7) = 21$$

Question 2

Given the price-demand function $$p(x) = 75 - 3x$$, what is the revenue function $$R(x) in $$terms of $$x$$?

Accepted Answer

$$R(x) = 75x - 3x^2$

Question 3

A car rental company charges according to the function $$C(x) = \begin{cases} 50x & 0  7 \end{cases}$$, where $$x is $$the number of days rented. What is the cost of renting a car for 5 days?

Accepted Answer

$$C(5) = 230$$

Question 4

Suppose the supply of barley is modeled by the equation $$p = 2.8 + 0.0002x$$, where $$p is $$the price per bushel and $$x is $$the number of bushels. What is the price per bushel when the supply is 7,900,000 bushels?

Accepted Answer

Question 5

A company has fixed costs of $$300 per day and total costs of 5$$,100 per day at a daily output of 200 boards. Assuming total cost per day $$C(x) is $$linear in $$x$$, what is the cost function $$C(x)$$?

Accepted Answer

$$C(x) = 300 + 24x$$

Question 6

Find the average cost per board for the company in the previous question if $$x = 30$$ boards are produced per day.

Accepted Answer

$$\frac{C(30)}{30} = \frac{300 + 24 	imes 30}{30} = 34$$

Question 7

Suppose $$2,500 is $$invested at $$7	ext{\%}$$ compounded quarterly. How much money will be in the account after $$15$$ years?

Accepted Answer

$$A = 2,500 	imes (1 + 0.07/4$$)^{60}$$ \approx 7,200$$

Question 8

If $$f(x) = \frac{1}{x^2$ + 4}$$, which of the following best describes the end behavior of $$f(x) as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 9

Given the function $$h(x) = -x^2$ + 2x + 8$$, what is the vertex of the parabola?

Accepted Answer

$$(1, 9)$$

Question 10

A graph of $$g(x) is $$shown with a jump discontinuity at $$x = 2. $$What is $$\lim_{x 	o 2} g(x)$$?

Accepted Answer

The limit does not exist

Question 11

Evaluate $$\lim_{x 	o 5} \frac{x}{x^2$ - 25}.$$

Accepted Answer

$$\frac{5}{0} ($$undefined)

Question 12

Find $$\lim_{x 	o 4} \sqrt{x + 4}.$$

Accepted Answer

$$\sqrt{8}$$

Question 13

A mutual fund earns an average annual return of $$9.58\%$$ compounded annually. How long (to the nearest year) will it take for the money invested to double?

Accepted Answer

$$t = \frac{\ln 2}{\ln(1.0958)} \approx 8$$

Question 14

Given $$f(x) = \frac{x^2$ + 7x + 10}{x^2$ - x - 20}$$, find $$\lim_{x 	o 5} f(x).$$

Accepted Answer

$$\frac{50}{0} ($$undefined)

Question 15

A company’s revenue function is $$R(x) = 75x - 3x^2$. For what value of x$ is the revenue maximized?

Accepted Answer

$$x = 25$$

Question 16

Suppose the price-supply equation for barley is $$p = 2.8 + 0.0002x$$ and the price-demand equation is $$p = 2.57 - 0.0001x. $$What is the equilibrium quantity $$x$$?

Accepted Answer

$$x = 2,300,000$$

Question 17

Find $$\lim_{x 	o 1} \frac{x^2$ - x - 2}{x^2$ - 4x - 21}.$$

Accepted Answer

$$\frac{-2}{-24}$$

Question 18

If $$C(x) is $$the total cost function and $$C(x) is $$linear, which of the following statements is always true?

Accepted Answer

The marginal cost is constant

Question 19

A company’s cost function is $$C(x) = 300 + 24x. $$What is the marginal cost?

Accepted Answer

$$24$$

Calculus Practice Problems: Functions, Limits, and Applications

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