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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (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

C=3x%2B2500


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b)

To find the average cost, simply take the total cost (which is 3x%2B2500) and divide it by x like this

Average Cost:

A=%283x%2B2500%29%2Fx

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c)

Average cost for 10 animals

A=%283%2810%29%2B2500%29%2F%2810%29=%2830%2B2500%29%2F%2810%29=%282530%29%2F%2810%29=253


So the average cost per animal is $253

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Average cost for 100 animals

A=%283%28100%29%2B2500%29%2F%28100%29=%28300%2B2500%29%2F%28100%29=%282800%29%2F%28100%29=28


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.


A=%283x%2B2500%29%2Fx Start with the average cost function


3=%283x%2B2500%29%2Fx Plug in A=3


3x=3x%2B2500 Multiply both sides by x


0=2500 Subtract 3x from both sides


Since 0=2500 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)

A=%283x%2B2500%29%2Fx Start with the average cost function


5=%283x%2B2500%29%2Fx Plug in A=5


5x=3x%2B2500 Multiply both sides by x


2x=2500 Subtract 3x from both sides


x=1250 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