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Question 158736: 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?
Found 2 solutions by stanbon, yourtutorssuck:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
C(x) = 2500 + 3x 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.
[C(x)]/x = [2500 + 3x]/x
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c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals.
For 10 animals: [C(10)] = [2500 + 3*10]/10 = 2800/10 = 280 dollars
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You can do the work for x=100 and for x=1000
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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.
The horizontal asymptote is 3x/x = 3
The average would not drop below $3
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e. How many animals should be tested for the average cost to be $5.00 per animal?
Let C(x)=$5 and solve for "x":
5 = [2500+3x]/x
2x = 2500
x = 1250 animals.
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Cheers,
Stan H.
Answer by yourtutorssuck(1) (Show Source):
You can put this solution on YOUR website! 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.
3x+2500
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.
3x+2500 / x
c. Find the average cost per animal for 10 animals. 100 animals. 1,000 animals.
3(10)+2500/10 = 30+2500/10= 2530/10=$253
3(100)+2500/100 = 300+2500/100 = 2800/10=$28
3(1000)+2500 / 1000 = 3000+2500 / 1000= 5500 / 1000 = $5.50
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.
no
e. How many animals should be tested for the average cost to be $5.00 per animal?
5=3x+2500/x
first multiply by the denominator on both sides.
5x=3x+2500
now solve.
2x=2500
x=1250
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