Animal Population

Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are $3,500 for setup costs and $4.00 to administer each test. 

a. Write an expression that gives the total cost to test x animals. Explain.(3 pts) 

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. Explain. (3 pts) 

c. Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals. (3 pts) 

d. As the number of animals tested increases, what happens to the average cost to test the animals? How do you know this? (2 pts). 

e. Would the average cost ever fall below $4.00? If so, identify a value that supports your answer. If not, explain how you know. (4 pts) 

f. How many animals should be tested for the average cost to be $5.00 per animal? Make sure to show how you derived the answer. (4 pts) 

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

a. Write an equation with P and A that could be used to solve for the constant of variation k. Explain. (Hint: No numbers are included) (3 pts) 

b. A biologist counted 30 white tail deer in a 200-acre parcel of land in a nature preserve. Find the constant of variation k. (4 pts) 

c. If the entire nature preserve is 3000 acres, then what is the total white tail deer population in the preserve? Describe how you arrived at your answer. (4 pts)