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# P3 - Can someone check my method please? watch

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1. 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)

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)
2. (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)

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.
3. (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...
4. Looks fine.
5. (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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