Gas Tank Leak Rate Problem: Modeling and Calculating with V(t)=90(1-t/18)^2

[xdeanna]

The gas tank of a parked pickup truck develops a leak. The amount, V, in liters, of gas remaining in the tank after t hours can be modeled by the function
V(t)= 90(1-t/18)^2 , t is between 0 and 18.

b) how fast is the gas leaking from the tank at t=12h

I tried V(12) and V'(12) but still didn't get the answer at the back of the book. Shouldn't it be the first derivative at t=12?

 

[Quinzio]

The gas tank of a parked pickup truck develops a leak. The amount, V, in liters, of gas remaining in the tank after t hours can be modeled by the function
V(t)= 90(1-t/18)^2 , t is between 0 and 18.

b) how fast is the gas leaking from the tank at t=12h

I tried V(12) and V'(12) but still didn't get the answer at the back of the book. Shouldn't it be the first derivative at t=12?

Yes, you should compute
$$\frac{dV}{dt}$$
and evaluating for t =12

You should get 3.33 l/h

 

[xdeanna]

Thanks :) I got that too.. the book is wrong