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?
The question in imcomplete. The cost y of testing n alligators is
y = 2500 + 3n.
The cost, in millions of dollars, to remove x % of pollution in a lake modeled by
a. The expression that gives the total cost to test x animals can be written as:
Total cost = setup cost + (number of animals * cost per test)
In this case, the setup cost is $2,500 and the cost per test is $3.00. Thus, the expression is:
Total cost = $2,500 + ($3.00 * x)
b. The expression that gives the average cost per animal can be written as:
Average cost per animal = Total cost / number of animals
Using the expression from part a, we get:
Average cost per animal = ($2,500 + ($3.00 * x)) / x
c. To find the average cost per animal for different numbers of animals, substitute the value of x in the expression from part b.
For 10 animals:
Average cost per animal = ($2,500 + ($3.00 * 10)) / 10
Average cost per animal = ($2,500 + $30) / 10
Average cost per animal = $2,530 / 10
Average cost per animal = $253
For 100 animals:
Average cost per animal = ($2,500 + ($3.00 * 100)) / 100
Average cost per animal = ($2,500 + $300) / 100
Average cost per animal = $2,800 / 100
Average cost per animal = $28
For 1,000 animals:
Average cost per animal = ($2,500 + ($3.00 * 1000)) / 1000
Average cost per animal = ($2,500 + $3,000) / 1000
Average cost per animal = $5,500 / 1000
Average cost per animal = $5.50
d. As the number of animals tested increases, the average cost per animal tends to decrease. This is because the fixed setup cost is spread over a larger number of animals. However, the average cost will never fall below $3.00, as each test incurs a cost of $3.00.
e. To find the number of animals required for the average cost to be $5.00 per animal, we can set up the following equation:
($2,500 + ($3.00 * x)) / x = $5.00
Simplifying the equation:
$2,500 + ($3.00 * x) = $5.00 * x
$2,500 = $5.00 * x - $3.00 * x
$2,500 = $2.00 * x
x = $2,500 / $2.00
x = 1,250 animals
Therefore, 1,250 animals should be tested for the average cost to be $5.00 per animal.