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Math Help - rate of change help

  1. #1
    Junior Member
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    rate of change help

    water flows into a dam at a rate given by dv/dt = 30000 root (t+1)

    Find the expression for the volume of water in the dam after t days assuming that the dam initially held 60000 m^3 of water

    i tried integration of this equation
    30000 root(t+1) + 60000

    but i couldnt get the right answer which was 2000[2 + (t+1)^1.5]
    any help greatly appreciated !
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  2. #2
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    Quote Originally Posted by flyinhigh123 View Post
    water flows into a dam at a rate given by dv/dt = 30000 root (t+1)

    Find the expression for the volume of water in the dam after t days assuming that the dam initially held 60000 m^3 of water

    i tried integration of this equation
    30000 root(t+1) + 60000

    but i couldnt get the right answer which was 2000[2 + (t+1)^1.5]
    any help greatly appreciated !

    HI

    I think the answer should be V=20000[2+(t+1)^{\frac{3}{2}}]

    you integrated wrongly

    \frac{dv}{dt}=30000(t+1)^{\frac{1}{2}}

    V=30000\int (t+1)^{\frac{1}{2}}

    =  20000(t+1)^{\frac{3}{2}}+c

    When t=0 , V=60000

    put that in , and you will find that c is 40000

    Then simplify ..
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  3. #3
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    thankyouu !!
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