SOLUTION: 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 $2,750 for setup costs and $4.50 to adminis

Question 568455: 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 $2,750 for setup costs and $4.50 to administer each test.
a. Write an expression that gives the total cost to test x animals.
So far I have C(x)/x = 2750(4.5)/x...but I am not confident that is the right expression.
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. x should be the only variable.
Wouldn't that be the answer I just stated above??
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 $4.50? 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 $9.50 per animal?
If I could understand the concept behind this rational expression exercise I can probably answer the last two (d and e) by myself. Am I right with my initial attempt at the expression? If not, can you please show me where I am wrong and explain it? Thanks in advance!
Answer by KMST(893) (Show Source):
You can put this solution on YOUR website!
Before testing any animals, you spend $2,750. You need to spend that much to buy equipment before you start. You can use that equipment over and over, once you catch your first alligator, but you cannot start without that initial expense.
So for you already spent .
Testing each animal costs and additional $4.50. So for one animal you spend $4.50, after the initial $2750 you had to spend just to start. If you tested 10 animals, it would cost the initial $2,750, plus $45 ($4.50 times 10).
So, if you test x aminals you will spend $ in addition to the $2,750 you had spend for set up before you started testing animals.
The total cost for testing those animals is

The answer to part a. is
b. The average cost per animal is