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Algebra

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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, 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?

  • Algebra - ,

    a. C = 2500 + 3X.

    b. Avg = ( 2500 + 3X ) / X

    c. Avg = ( 2500 + 3*10 ) / 10 = 253
    Avg = ( 2500 + 3*100 ) / 100 = 28
    Avg = ( 2500 + 3*1000 ) /1000 = 5.5

    d. Decreases. No. Rearranginging
    equation: Avg = 2500 / x + 3X/X
    As X increases, the first term
    approaches 0; but 2nd term re-
    mains constant at 3. Therefore
    the min. is 3.

    e. Avg = ( 2500 + 3X ) / X = 5.00
    Solve for X by multiplying both
    sides by X: 2500 + 3X = 5X,
    2X = 2500, X = 1250.

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