Question 325938: Biologists want to set up a station to test alligators in the lake for the West Nile Virus. Suppose that the costs for such a station are $2500 for set up costs and $3.00 to administer each test.
A> write an example that gives the total cost to tet animals
B> You can find the average cost per animal by dividing total costs by the 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 1000 animals.
D> As the number of animals tested increase, 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, how come?
E> How many animals should be tested for the average cost of the test to be $5.00 per animal?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Biologists want to set up a station to test alligators in the lake for the West Nile Virus. Suppose that the costs for such a station are $2500 for set up costs and $3.00 to administer each test.
A> write an example that gives the total cost to test animals
let number of animals be x
the cost to test animals will be 2500+3x
B> You can find the average cost per animal by dividing total costs by the number of animals. write the expression that gives the average cost per animal.
Average cost per animal = (2500+3x)/x
C> Find the average cost per animal for 10 animals, 100 animals, and 1000 animals.
plug the value of 10, 100, 1000 in the expression.
The average cost will be
(2500+30)/10=$253 for 10 animals
(2500+300)/100=$28 for 100 animals
(2500+3000)/1000 = $ 5.5 for 1000 animals
D> As the number of animals tested increase, 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, how come?
If average cost is to be less than 3
(2500+3x)/ x < 3
multiply by x
(2500+3x)*x /x < 3*x
(2500+3x)<3x
Add -3x
2500+x-x< 3x-3x
2500<0 this is not valid.
since the variable cost is $3 the average cost can never be less than $3 since fixed cost have to be added
E> How many animals should be tested for the average cost of the test to be $5.00 per animal?
(2500+3x) / x= 5
2500+3x =5x
2500=5x-3x=2x
x=1250 animals
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