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 $6,000 for setup costs and $5.00 to adminis

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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 $6,000 for setup costs and $5.00 to adminis      Log On

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Question 229403: 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 $6,000 for setup costs and $5.00 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 $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 $9.00 per animal?
Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
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 $6,000 for setup costs and $5.00 to administer each test.
a. Write an expression that gives the total cost to test x animals.
Total cost = 6000 + 5x dollars
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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.
Average cost = (6000+5x)/x dollars
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c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals.
Comment: Let x = 10 ; then x = 100 ; then x = 1000
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d. As the number of animals tested increases, what happens to the average cost to test the animals?
The average cost decreases
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Would the average cost ever fall below $5.00? If so, identify a value that supports your answer. If not, explain how you know.
Solve (6000+5x)/x < 5
6000+5x < 5x
6000 < 0
That is a contradiction, so the average can never be less than $5.
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e. How many animals should be tested for the average cost to be $9.00 per animal?
Solve (6000+5x)/x < 9
6000+5x < 9x
6000 < 4x
x > 1500
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Cheers,
Stan H.