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?
Please post what you know about these problems and what you're having trouble with. Then we can help you.
tc=total cost
a. 2500+(3x)=tc
b. (2500+(3x))/x or tc/x
c. 10= $253 per animal
100= $28 per animal
1000= $5.50 per animal
d. As the amount af animals increase the price decreases and the average price will never fall below $3.00
e. (2500+(3x))/x=5
x=1250
a. The total cost to test x animals can be calculated using the expression:
Total cost = Setup cost + (Number of animals * Cost per test)
= $2,500 + ($3 * x)
b. The expression that gives the average cost per animal can be calculated by dividing the total cost by the number of animals:
Average cost per animal = Total cost / Number of animals
= ($2,500 + ($3 * x)) / x
c. To find the average cost per animal for different numbers of animals, we substitute the given values into the expression from part b:
For 10 animals:
Average cost per animal = ($2,500 + ($3 * 10)) / 10
= ($2,500 + $30) / 10
= $2,530 / 10
= $253
For 100 animals:
Average cost per animal = ($2,500 + ($3 * 100)) / 100
= ($2,500 + $300) / 100
= $2,800 / 100
= $28
For 1,000 animals:
Average cost per animal = ($2,500 + ($3 * 1,000)) / 1,000
= ($2,500 + $3,000) / 1,000
= $5,500 / 1,000
= $5.50
d. As the number of animals tested increases, the average cost to test the animals decreases. This is because the fixed setup cost of $2,500 is spread over a larger number of tests.
The average cost per animal would never fall below $3.00 because each test costs $3.00. The setup cost of $2,500 ensures that even if no animals are tested, the average cost will not go below $3.00.
e. To find the number of animals that should be tested for the average cost to be $5.00 per animal, we set up the expression from part b and solve for x:
$5.00 = ($2,500 + ($3 * x)) / x
Multiplying both sides by x:
$5.00 * x = $2,500 + ($3 * x)
$5.00 * x - $3 * x = $2,500
$2.00 * x = $2,500
Dividing both sides by $2.00:
x = $2,500 / $2.00
x = 1,250
Therefore, 1,250 animals should be tested for the average cost to be $5.00 per animal.