Question

Would you please check my answer to make sure I did it right?

Bus travel, a bus company finds that monthly costs for one particular year were given by C(t) = 100 + t^2 dollars after t months. After t months the company had P(t) =1000 +t^2 passengers per month. How fast is its cost per passenger changing after 6 months?

I did c and p prime
C'(t) = 2t
P'(t) = 2t

then i put it into the quotient form
(2t) (1000+ t^2) - (100 + t^2) (2t)/(1000 + t^2)^2

the answer i got was 0.010786021
Please tell me if this is not right. Thank you!

Answer 1

Since both C and P are monthly amounts, I will assume we are looking for the monthly cost per passenger. That would, of course, be

C/P = (100+t^2)/(1000+t^2)

As you say, (C/P)' = 1800t/(1000+t^2)^2

So, at t=6, (C/P)' = 0.01006246

Close, but I wonder what happened down in the details.