SOLUTION: 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 $2,500 for setup costs and $3.00 to adminis

Question 166192: 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 $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. 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.
e. How many animals should be tested for the average cost to be $5.00 per animal?

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
OK we are given fixed cost of 2500. Lets call total cost C and the number of animals A. We are given an additional cost of $3.00 for each test administered to an animal.
a. so to express total cost to test A animals we have

b. Average cost per animal would be total cost divided by total number of animals
c For 10 animals we have (2500+3(10)/10= $253/animal
For 100 animals we have (2500+3(100)/100= $28/animal
For 1000 animals we have (2500+3(1000)/1000= $5.4/animal
d. the avg cost per animal decreases as the amount of animals increases.
the avg cost per animal will never go below 3--->avg cost =(2500+3A)/A
or (2500/A)+3 so it can get close to $3/animal but never quite reachs it.
e (2500+3A)/A=5 so 2A=2500 A=1250 animals to avg $5 in costs
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