1) The cost, in millions of dollars, to remove x % of pollution in a lake modeled by (Hint: if it is 20%, substitute 20 instead of x, not 20% or 0.2). Round your answers to the nearest tenth (of a million).
A) What is the cost to remove 45% of the pollutant?
B) What is the cost to remove 72% of the pollutant?
C) What is the cost to remove 96% of the pollutant?
D) For what value is this equation undefined?
E) Do the answers to sections a. through d. match your expectations? Explain why or why not.
2) 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 $5,100 for setup costs and $4.50 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 15 animals, 150 animals, and 1,500 animals. Round your final answers to the nearest cent.
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 $5.00? If so, identify a value that supports your answer. If not, explain how you know.
E) How many animals should be tested for the average cost to be $21.00 per animal?
3) 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 and inversely proportional to the average distance to a source of fresh water (in miles). [Hint: Carefully review Section 6.9 of the assigned readings before attempting this problem]
A) Write an equation using only three variables that could be used to solve for the constant of variation k
B) A biologist counted 27 white tail deer in a 100-acre parcel of land in a nature preserve, where the average distance to a source of fresh water was 0.4 mi. Find the constant of variation k
C) If the entire nature preserve is 9,500 acres, then what is the total white tail deer population in the preserve, assuming the average distance to a source of fresh water within the preserve is 1.2 mi? Describe how you arrived at your answer