Question 1

Given the quadratic function $$y = 2x^2$ - 6x - 1$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = \frac{6 \pm \sqrt{44}}{4}$$

Question 2

A company charges $$150 for a seminar and attracts 800 people. For each 10 $$decrease in price, it attracts 80 additional people. What price maximizes revenue?

Accepted Answer

$$90$$

Question 3

Suppose revenue in dollars is given by $$R(x) = -x^2$ + 80x$$ and cost is $$C(x) = x^2$ + 192. $$What is the minimum break-even quantity?

Accepted Answer

$$x = 8$$

Question 4

For the revenue function $$R(x) = -x^2$ + 80x$$, at what value of $$x is $$the maximum revenue achieved?

Accepted Answer

$$x = 40$$

Question 5

Given the demand function $$p = -0.72x + 51$$, what is the revenue function $$R(x)$$?

Accepted Answer

$$R(x) = -0.72x^2$ + 51x$$

Question 6

The cost of producing $$x$$ thousand units of a product is $$C(x) = 2.23x^2$ + 3.5x + 85. $$What is the profit function $$P(x) if $$the revenue is $$R(x) = -0.72x^2$ + 51x$$?

Accepted Answer

$$P(x) = -2.95x^2$ + 47.5x - 85$$

Question 7

For what values of $$x is $$production profitable, given $$P(x) = -2.95x^2$ + 47.5x - 85$$?

Accepted Answer

$$2 \u003c x \u003c 17$$

Question 8

If the cost of manufacturing $$q$$ units is $$C(q) = q^2$ + 50q + 200$$, what is the cost of manufacturing the 10th unit?

Accepted Answer

$$C(10) - C(9) = 320$$

Question 9

A manufacturer produces cassettes at a cost of $$2 per cassette. If the price is increased by 1$$, 400 fewer cassettes will be sold each month. What is the profit function in terms of price $$p$$?

Accepted Answer

$$P(p) = (6,000 - 600p)(p - 2)$$

Question 10

At what price is the manufacturer's monthly profit maximized for the cassette problem above?

Accepted Answer

$$p = 5$$

Question 11

If $$800 is $$invested in an account earning $$3.15\%$$ compounded continuously, what is the amount after $$4$$ years?

Accepted Answer

$$A = 800e$$^{0.126}$$

Question 12

Write the equation $$5^x = \frac{1}{25} in $$logarithmic form.

Accepted Answer

$$x = \log_5$ \left(\frac{1}{25}\right)$$

Question 13

Evaluate $$\ln\left(\frac{1}{e^4$}\right).$$

Accepted Answer

$$-4$$

Question 14

Write $$\log_2$\left(\frac{x^3$}{y^3$}\right) as a $$sum, difference, or product of simpler logarithms.

Accepted Answer

$$3\log_2$ x - 3\log_2$ y$$

Question 15

If $$A = 4400\left(1 + \frac{0.025}{4}\$$right)^{4 	imes 5}$$, what is the total amount after 5 years?

Accepted Answer

$$A = 5172.97$$

Question 16

Given $$3^y = (3$$)^{-4}$$, what is the value of y$?

Accepted Answer

$$y = -4$$

Question 17

Suppose the total cost in dollars of manufacturing $$q$$ units is $$C(q) = q^2$ + 50q + 200. $$What is the cost of manufacturing the 10th unit?

Accepted Answer

$$C(10) - C(9) = 320$$

Question 18

If the revenue function is $$R(x) = -x^2$ + 80x$$ and the cost function is $$C(x) = x^2$ + 192$$, what is the maximum profit?

Accepted Answer

$$864$$

Nonlinear Functions and Applications in Business Calculus

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