2. Biologists want to set up a station to test alligators in the lake for West N
ID: 3099177 • 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
The best way to translate words to equations is to figure out what your factors are. Example: in your problem, the factors are set up costs and administration costs per test, which comprise the total costs for the testing station. Setup Costs = $2500 (setup infers a one time cost) Admin Cost = $3 per Test a. The first question is to write an expression that gives total cost to test a certain number of animals. First thing to do here is recognize the factors in your word problem in the question being asked and create your expression from there. total costs = (admin cost per test * # of animals tested) + $2500 setup cost or, TC = 3x + 2500 b. Average cost? Same thing. Recognize factors in the question asked. Avg Cost per Animal = (total costs) / number of animals tested, or, Avg Cost/Animal = ((admin cost per test * # of animals tested) + $2500 setup) / # of animals tested, or, Avg Cost = (3x + 2500)/x c. Find the average cost/animal for 10, 100, and 1,000 animals. Use the formula above: Avg = (3(10) + 2500)/10 Avg = (30+2500)/10 Avg = 2530/10 Avg = $253 per animal for 10 , $28 per animal for 100, etc. d. As the # of animals increases, could the avg cost ever fall below $3? If so, identify, if not, explain. Well, this is pretty self explanatory to me. If one of the factors in total cost is a $3 admin cost per animal and it also contains at least *part* of the $2500 setup cost, it could never fall *below* the actual admin cost per test. e. How many animals should be tested for the avg cost to be $5/animal? Use the same formula we established earlier [Avg Cost = (3x + 2500)/x], just replacing the Avg Cost with your target they give you. If Avg Cost = (3x + 2500)/x, then $5 = (3x + 2500)/x, and like above, x still represents the # of animals tested. 5 = (3x + 2500)/x, distribute x to both sides. 5x = 3x + 2500, distribute 3x isolate x. 2x = 2500, or x = 1250 animals to be tested for an average cost of $5/animal. :)
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