Fuel is burnt at a rate dV/dt=100e^0.04t where V is the volume of the fuel is litres, and t is measured in hours.

Question

(i) At what rate is fuel burning when t = 4 hours? Ans = ___ L/h

(ii) How much fuel is burnt during the first week? Ans = ___ L/h

Answer 1

(i) Plug t=4 into dV/dt

 

dV/dt|₄ = 100e^0.04(4) = ?

 

(ii) Integrate dV/dt from 0 to the length of a week, which is 7(24) = 168 hours

 

ΔV = amount of fuel burned

 

ΔV = ∫₀¹⁶⁸ (100e^0.04t)dt = ?

 

You should be able to finish from here.