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 $3,000 for setup costs and $4.00 to administer each test.
a. Write an expression that gives the cost(C) to test animals.
b. you can find the average cost per animal by dividing total costs by number of animals. Write the equation that gives the average cost (AC) per animal.
c. Find the average cost for 20 animals.
d. Find the average cost for 200 animals.
e. Find the average cost for 2000 animals.
f. How many animals should be tested for the average cost to be $5.00 per animal?
a. C = 4X + 3000.
b. AC = (4X + 3000) / X.
c. AC = (4*20 + 3000) / 20 = $154.
d.
e.
f. AC = (4X + 3000) / X = $5.00,
Multiply both sides by x:
4X + 3000 = 5X,
5X - 4X = 3000,
X = 3000 Animals.
a. The expression that gives the cost (C) to test animals can be calculated by multiplying the number of animals (n) by the cost per test ($4.00) and adding the setup costs ($3,000). So the expression is:
C = (4 * n) + 3000
b. The equation that gives the average cost (AC) per animal can be found by dividing the total costs (C) by the number of animals (n). So the equation is:
AC = C / n
c. To find the average cost for 20 animals, we substitute n = 20 into the equation:
AC = (4 * 20 + 3000) / 20
AC = (80 + 3000) / 20
AC = 3080 / 20
AC = $154.00
d. To find the average cost for 200 animals:
AC = (4 * 200 + 3000) / 200
AC = (800 + 3000) / 200
AC = 3800 / 200
AC = $19.00
e. To find the average cost for 2000 animals:
AC = (4 * 2000 + 3000) / 2000
AC = (8000 + 3000) / 2000
AC = 11000 / 2000
AC = $5.50
f. To find out how many animals should be tested for the average cost to be $5.00 per animal, we can set up the equation:
5 = (4 * n + 3000) / n
Simplifying the equation:
5n = 4n + 3000
n = 3000
So, 3000 animals should be tested for the average cost to be $5.00 per animal.