Thread: V=A(1-e^-kt). Finding fraction of V after a period of time.

1. V=A(1-e^-kt). Finding fraction of V after a period of time.

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.

2. Originally Posted by 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.
What does A stand for in this equation?

3. Originally Posted by 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.
Start by noting that the capacity of the vessel is A (since V ---> A as t ---> +oo). Therefore V = A/4 when t = 5. Use this to solve for k.

Now find (in terms of A) V when t = 10 etc.