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 140638: 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 jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)

In this case, the startup cost ($2,500 ) is the fixed cost and the cost to administer each test ($3.00 ) is the variable cost

Also, remember the cost function in general is

Cost = variable cost*x + fixed cost

So in our case, the cost function is

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b)

To find the average cost, simply take the total cost (which is ) and divide it by x like this

Average Cost:

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c)

Average cost for 10 animals

So the average cost per animal is $253

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Average cost for 100 animals

So the average cost per animal is $28

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Average cost for 1,000 animals

So the average cost per animal is $5.50

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d)

As the number of animals tested increases, the average cost per animal decreases.

Start with the average cost function

Plug in

Multiply both sides by x

Subtract 3x from both sides

Since will never be true, this means that the average cost will never be equal to $3. So this also means that the average cost will never fall below $3 (since it never gets to $3)

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e)

Start with the average cost function

Plug in

Multiply both sides by x

Subtract 3x from both sides

Divide both sides by 2 to isolate x

So 1,250 animals must be tested to make the average cost to be $5.00 per animal
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