MAT 117 B Project 2 Management of Infectious Diseases in Wildlife

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 Filemenu. Click the white space below each question to maintain proper formatting.

Please show all of your work.

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.

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

1. 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.

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

1. 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.

1. How many animals should be tested for the average cost to be $5.00 per animal?

1. 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.

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

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

1. 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.

1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by.

              Note: (for the following questions, you must substitute .75, .9, and .99 for x)

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

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

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

1. For what value is this equation undefined?

1. Note that if all of the pollution is removed (100%, or 1.0 per unit), the equation becomes a divide-by-zero situation which is now interpreted as undefined but can also be stated as approaching an infinite cost.  Please state why you think that this is or is not a credible representation of a natural phenomenon.