Volume Question - dN/dt = k(N-P) (1 Viewer)

[Lukybear]

A vessel is being filled at a variable rate and the volume of liquid in the vessel at any time t is given by:

V=A(1-e^-kt)

b) If one quarter of the vessel is filled in 5 minutes, what fraction is filled in the next five minutes.

 

[gsd]

when t=5, V=A/4
1-e^(-5k)=1/4
e^(-5k)=3/4

when t=10
V=A(1-e^(-10k))
=A(1-e^(-5k)^2)
=A(1-(9/16))
=7A/16

(7A/16)-(A/4)=3A/16
hence 3/16 filled