Pre Calculus Help due tonight please help!!!

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MATH233 Unit 3: Exponential Functions

Discussion Board Assignment: Version 2A

Note: All work must be shown and explained to receive full credit.

Suppose that you established a startup company that develops a gaming application, and based on

preliminary studies, the demand for your product is given by the following function:

𝑃(𝑥) = 𝑘𝑒−𝑟𝑥

where P is the price in U.S. dollars per download of the application, and x is the number of downloads.

1. Begin to set up the demand function of your product by choosing a value for k based on the first

letter of your last name. Make sure to choose a unique value, one that is different from what your

classmates have chosen. (Note: The value for k does not necessarily have to be a whole number.)

First letter of your last name Possible values for k

A–F 110–200

G–L 210–300

M–R 310–400

S–Z 410–500

2. Complete the setup of your demand function by choosing a value for r based on the first letter of

your last name. Make sure to choose a unique value, one that is different from what your

classmates have chosen.

First letter of your last name Possible values for r

A–F 0.000100–0.000299

G–L 0.000300–0.000499

M–R 0.000500–0.000699

S–Z 0.000700–0.000899

3. Set up the revenue function, R(x), of your application if R(x) = xP(x).

4. Find your company’s revenue given the following number of downloads:

Number of downloads (x) R(x)

100

500

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1,000

5,000

5. What is your marginal revenue function? (Show intermediate steps.)

6. How many downloads should the application have to reach its maximum revenue? (Show your

work.)

7. What is your maximum revenue? (Show your work.)

8. Sketch a graph of the revenue function to verify your answer in Step 7. Use Excel or another

graphing utility. If necessary, insert your graph into a Word document and attach the Word

document to the DB thread.

9. What price for your game would yield the maximum revenue? (Show your work.)

10. What is the rate of change of the revenue when there are 1,000 downloads? (Show your work.)

11. Compare the price of your application and your company’s revenue to one of your classmates’

calculations.

12. Why is it important to analyze the price of your gaming application and the revenue that you will

generate?

13. Which intellipath Learning Nodes helped you with this assignment?