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P3 - Can someone check my method please? watch

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    Ok, seems like I prefer maths when there are no words involved so this forming an equation thing is not ideal for me. Can some please check that I havent broken any major rules of maths here...

    Question

    At time, t, the rate of increase in the concentration , C, of a mico-organism is equal to kC, (k being a positive constant). When t=0, C=C0

    a) Form and solve a fifferential equation to show that C = C0(e^kt)


    My Answer

    dC/dt = kC

    => [between C and C0] 1/C dC = ∫ [between t and 0] k dt
    => [ln C - lnC0] = [kt]
    => ln(C/C0) = kt
    => C/C0 = e^kt
    => C = C0(e^kt)
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    (Original post by Leekey)
    Ok, seems like I prefer maths when there are no words involved so this forming an equation thing is not ideal for me. Can some please check that I havent broken any major rules of maths here...

    Question

    At time, t, the rate of increase in the concentration , C, of a mico-organism is equal to kC, (k being a positive constant). When t=0, C=C0

    a) Form and solve a fifferential equation to show that C = C0(e^kt)


    My Answer

    dC/dt = kC

    => [between C and C0] 1/C dC = ∫ [between t and 0] k dt
    => [ln C - lnC0] = [kt]
    => ln(C/C0) = kt
    => C/C0 = e^kt
    => C = C0(e^kt)
    Yep, you've done it fine. Could have done it without the limits and just found out the constant using those values, but there's nothing wrong with your method.
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    (Original post by Nylex)
    Yep, you've done it fine.
    Thank god for that, I can never get my head around putting the limits in the correct way round etc... I always seem to end up with something horrendus so when I got something that looked right, I assumed I'd cheated...
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    Looks fine.
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    (Original post by Leekey)
    Thank god for that, I can never get my head around putting the limits in the correct way round etc... I always seem to end up with something horrendus so when I got something that looked right, I assumed I'd cheated...
    Lol .
 
 
 
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