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Math 1613 Homework #11

Name:

1. The level of contamination in a certain lake is

f(p) =

√

p parts per million

when the population of the surrounding community is p people. The population of the surrounding

community in year t is modeled as

p(t) − 400t2 + 2500 people

where t is the number of years since 2000. Write a single model that gives the level of contamination in

year t.

2. Party Fun, Inc. manufactures and sells inflatable bounce toys of the type used at events such as festivals

and children’s parties. The total cost to produce x moonwalk castles in a year is modeled as

C(x) = 600x + 90000 dollars.

The revenue from the sale of x moonwalk castles is modeled as

R(x) = 1800x dollars.

Write a single model that gives the profit from producing and selling x moonwalk castles.

3. A movie theater charges $9 for adults and $7 for seniors. On a particular day when 331 people paid

an admission, the total receipts were $2517. Find how many of each type of ticket was sold. Use the

substitution method.

Wells 1613 Mini Project 6 Name:

Directions: For this 6th project, I want you to use your knowledge of rational models to answer questions

about the provided model. You will submit your work through Blackboard.

1. Queuing theory (also known as waiting-line theory) investigates the problem of providing adequate

service economically to customers waiting in line.

Suppose that at a certain fast food restaurant customers arrive at the rate of 9 people per hour. Then

we can model the average time (in hours) that a customer will wait in line before being served as

f(x) =

9

x(x − 9)

hours,

where x is the average number of people served per hour. (Note: 9 people arrive each hour, x people

are served each hour)

(a) Find f(15).

(b) Interpret your answer for part a in the context of this problem.

(c) Find f(7).

(d) Why is the function meaningless if the average number of people served per hour is less than 9?

(e) Suppose that once they have reached the front of the line the average time to serve a customer is 5

minutes. How many customers can be served in an hour? How many minutes will a customer have

to wait in line on average?

(f) Use Desmos to graph the function. Adjust the viewing window. Save your Desmos graph.

(g) What is the equation of the vertical asymptote?

(h) What is the equation of the horizontal asymptote?

(i) Suppose that the average wait time is 7.5 minutes (1/8 hour). How many customers are served per

hour on average?

2. Submit your answers on Blackboard as a Word document and your Desmos graph.

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