Question 277935
problem a:


c = 3*x + 2500


c is the total cost for setting up the station and administering the tests.


problem b:


a = (3*x+2500)/x


a is the average cost to test each animal.


that's the total cost divided by the number of animals tested.


problem c:


average cost for 10 animals is (3*10 + 2500)/10 = 2530/10 = $253.00


average cost for 100 animals is (3*100) + 2500)/100 = 2800/10 = $28.00


average cost for 1000 animals is (3*1000) + 2500)/1000 = 5500/1000 = $5.50


problem d:


average cost per animal goes down.


it will never go below $3.00 per animal.


as x gets larger, the percentage of 2500 / x gets smaller.


it can approach 0 but it will never be 0.


if it was 0, the average cost would be (3*x)/3 = $3.00


anything above that makes the average cost just a little bit higher than $3.00, but never below that.


example:


(3*(1 billion) + 2500)/1 billion equals:


3*(1 billion)/1 billion + 2500/(1 billion) which equals:


3 + (2500/(1 billion).


now 2500 / 1 billion is a very small number, but it is not equal to 0, so the average cost is going to be $3.00 + a very small number.


problem e:


the formula for average is:


a = (3*x + 2500)/x


set a = 5 and this formula becomes:


5 = (3*x + 2500)/x


multiply both sides of this equation by x to get:


5*x = 3*x + 2500


subtract 3*x from both sides of this equation to get:


2*x = 2500


divide both sides of this equation by 2 to get:


x = 1250


at 1250 tests, the average cost should be $5.00 per test.


plug this into the original equation for average to see if it holds.


a = (3*x + 2500)/x becomes:


a = (3*1250 + 2500) / 1250 which becomes:


a = 3750 + 2500) / 1250 which becomes:


a = 6250 / 1250 which becomes:


a = 5


the average cost per test of $5.00 is confirmed to be true.