Question

In a gas station, petrol is pumped into a tank at a rate of \[dV/dt=t ^{3/2} m^3/\min\] , where V is the volume of petrol in m3 and t is time in minutes.

(a) Find the volume of petrol in the tank after t minutes. Given that the initial condition is V = 15 m3, when t = 0.

(b) If the capacity of the tank is 100 m3, how long does it take to fill up?

Answer 1

Well, I am here.
What do you think?

Answer 2

yup help

Answer 3

trying to catch you

Answer 4

is it b=15 m^3?

Answer 5

but how to calculate that equation

Answer 6

dV/dt= d{t^3/2+b/dt

Answer 7

OOOHO I am so so sorry!
I did not see that it tells the rate of change of V.
I thought it is just V(t).

So if we were given the rate of change of the volume, we can simply integrate it to get the function of the volume pumped in terms of time!