SOLUTION: 1.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 administ

Question 358472: 1.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, 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.
e.How many animals should be tested for the average cost to be $5.00 per animal?
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
1.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, 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.
e.How many animals should be tested for the average cost to be $5.00 per animal?

a.) total cost T = $2500 + $3 * A,
where $2500 is setup costs, $3 is cost per test, A is number of alligators
T = 2500 + 3A

b.) average cost C = T/A

c.) 10 alligators:
total cost T = 2500 + 3 * 10 = 2500 + 30 = $2530
average cost C = 2530/10 = $253 per alligator
100 alligators:
T = 2500 + 3 * 100 = 2500 + 300 = $2800
C = 2800/100 = $28 per alligator
1000 alligators:
T = 2500 + 3 * 1000 = 2500 + 3000 = $5500
C = 5500/1000 = $5.50 per alligator

d.) average cost goes down as the number of alligators is increased

average cost will approach $3.00 and will round to $3.00 but the lowest it will actually be is $3.00 plus a infinitesimally small fraction of a cent

average cost will never be below $3.00

number of alligators at average cost of $3.01:
3.01 = (2500 + 3A)/A
3.01A = 2500 + 3A
0.01A = 2500
A = 250,000 alligators at $3.01 average cost

e. number of alligators at average cost of $5.00
5 = (2500 + 3A)/A
5A = 2500 + 3A
2A = 2500
A = 1250 alligators

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