2. Biologists want to set up a station to test alligators in the lake for West N
ID: 3099051 • Letter: 2
Question
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, and 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?
Explanation / Answer
a: set x = number of animals, set y = cost for testing x animals x is controllable...test however many animals you want...it is an independent variable y is dependent on x...the dependent variable $3.00 per test is a rate per test, slope $2500 is a cost even if 0 tests are done, y intercept use slope intercept form y=mx+b => y = 3.00x + 2500 b: y/x = average cost per animal y/x = (3.00x + 2500) / x = 3.00 + 2500/x c: plug in numbers to the above equation 10 animals: y/x = 3.00 + 2500/10 = 253 100 animals: y/x = 3.00 + 2500/100 = 28 1000 animals: y/x = 3.00 + 2500/1000 = 5.50 d: this depends how you define $3.00 if $3.00 means that it has to round to 3.00 (3.004 for example) then we set y/x = 3.004 and solve for x 3.004 = 3 + 2500/x subtract 3 from both sides 0.004 = 2500/x multiply by x 0.004x = 2500 divide by 0.004 x = 2500/0.004 = 62500 or more animals if 3.0044444444444444444444444444444 then evaluate the same way and get x = 2500 / 0.004444444444444444444444 = 562500.0000000some small decimal so 562501 to be above that value if $3.00 is defined as having no decimals places (3.000000000000000000000000000000 infinite 0's repeating) then no, that can never happen because due to the $2500 set up fee there will always be a very tiny decimal some number of 0's down the line e: y/x = 5.00 5.00 = 3 + 2500/x subtract 3 from both sides 2 = 2500/x multiply by x 2x = 2500 divide by 2 x = 2500/2 = 1250
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.