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

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    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.
    Last edited by mr fantastic; May 22nd 2010 at 06:03 AM.
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    Quote Originally Posted by Lukybear View Post
    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?
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    Quote Originally Posted by Lukybear View Post
    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.
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