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

• May 22nd 2010, 01:06 AM
Lukybear
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.
• May 22nd 2010, 01:28 AM
e^(i*pi)
Quote:

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?
• May 22nd 2010, 06:06 AM
mr fantastic
Quote:

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.