# 2107162 mat117 Project 2 1 Student

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```					MAT 117 B Use Below pages Hints to Sole Project Two
Project 2
Management of Infectious Diseases in Wildlife

Most of the state of Minnesota is rural and agricultural. For comparison purposes, the population of the
Minneapolis – St. Paul area is about 3.5 million people, the population of Rochester, MN is about
105,000, and the population of Duluth, MN is less than 95,000. The remainder of the state is agricultural
and rural. The persons per square mile in Minnesota is 61.8 and for the entire US it is 79.6. For
comparison, Alabama is 87.7, Arizona is 45.2, and California is 217.2 persons per square mile. If you like
nature and want to get away from the hustle and bustle, consider Wyoming – 5.1 persons per square
mile.

There is a large natural wildlife population in the state of Minnesota and many different wild animals even
find their way into Minneapolis. It is not unusual to have black bears in suburban areas and bald eagles
are plentiful. Of course, everybody has to deal with coyotes.

Application Practice
Answer the following questions; please use Equation Editor to write mathematical expressions and
equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white
space below each question to maintain proper formatting.

Please note: if you copy answers directly from the Axia College Appendices, you
will get a wrong answer.

Please show your work. If you have a one word answer, please indicate the basis
for that one word answer.

1. Biologists in an agricultural county want to set up a station to test captured raccoons, fox, and
coyote for rabies. Suppose that the costs for such a station are \$2,500 for setup costs and \$3.00
to administer each test.

a. Write an expression that gives the total cost to test x animals.

b. You can find the average cost per animal by dividing total costs by number of animals.
Write the expression that gives the average cost per animal.

c.   Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals.

d. As the number of animals tested increases, what happens to the average cost to test the
animals? Would the average cost ever fall below \$3.00? If so, identify a value that
supports your answer. If not, explain how you know.

MAT/117
e. How many animals should be tested for the average cost to be \$5.00 per animal?

2. To estimate animal populations, biologists count the total number of animals in a small section of
a habitat. The total population of animals is directly proportional to the size of the habitat (in
acres) polled.

a. Write an equation that could be used to solve for the constant of variation k.

b. A biologist counted 12 white tail deer in a 100-acre parcel of land in a nature preserve.
Find the constant of variation k.

c.   If the entire nature preserve is 2,500 acres, then what is the total white tail deer
population in the preserve? Describe how you arrived at your answer.

One must be careful when presented with so-called scientific research and statistical analysis.
Numbers and tests can be manipulated by the way the data is presented or by the way that
equations are written. Consider the following example.

6,000
3. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C              .
2  2x
Note: (for the following questions, you must substitute .75, .9, and .99 for x)

a. What is the cost to remove .75 (75%) of the pollutant?

b. What is the cost to remove .90 (90%) of the pollutant?

c.   What is the cost to remove .99 (99%) of the pollutant?

6,000
d. For what numerical value is this equation ( C               ) undefined?
2  2x

MAT/117
Project 2 Hints Week 4

I know that if you take your time, don’t try to solve the whole thing at once,
and focus on each part of a problem you will be able to do this. If you allow
enough time, I believe that you will find this to be an easy 40 points.

Problem 1
1.a
If you don’t perform any tests, your cost is \$2,500. Let’s use C for cost.

If you don’t perform any test, your equation is: C = 2500.

So, if you perform 1 test your cost is: C = 2500 + 3(1).

If you perform x tests, your cost is: C = 2500 + ?; you have to decide what
should go where the ‘?’ is.

1.b
Hint: if 20 items cost \$100, then the average cost per item is \$5. How was \$5
calculated?

I’ll let you figure out 1.c and 1.d.

1.e
5 = (2500 + 3x)/x

Problem 2
For this problem refer to Section 6.9 and specifically look at Direct Variation.
2.a
Let A = the number of animals, and L = amount of land.

2.b
Apply your Direct Variation from 2.a.

2.c
Apply your Direct Variation from 2.a and your answer from 2.b.

Problem 3
3.a, b, c, d
Referring to the equation: C =
C is cost;
C=

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MAT/117

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