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[CrashOveride]

Logistic growth equation:

dP/dt = kP(1 - RP)
k, R are constants.


Show by differentiation that P = I / [RI + (1 - RI)e^-kt] , where I is the inital population (a constant), is a soluution of the logistic equation.


And also, just something i want to clear up:

I'll use an arbitary question:

For a body falling under gravity in air, the rate of change of velocity is given by dV/dt = -k(V - P) where P and k are constants. This has as a solution: V = P + Ae^-kt
If the rate of change is given by dV/dt = -0.02(V - 490)

part (a) tells us to derive an equation for V, remembering that initally V = 0. But why should the velocity be zero inititally ? What if a scenario came about where a body was already falling and when timing began, initially it had some z velocity ? Here the velocity initally would not be 0. And as the question doesn't say anything the body was inititally at rest when it was dropped etc. etc. how can we assume this, other than "remembering" it, as was asked of us. "Remembering" would imply that we should already know, just in case we forgot. Somebody correct me if i am brazenly wrong here or anywhere =p

part (b) went on to ask for the velocity after 10 seconds. Now, suppose it had asked us for the velocity after 10min. Or both. What 't' values would i be substituting here.

 

[CrashOveride]

Maybe the title is putting people off, but i cant seem to edit it.

 

[Affinity]

first question:
Hmm just differentiate and substitute, verify the LHS = RHS

second:

they are just setting t=0 when V=0, maths still work if you use some other values, but stick with what they give you for the question.

stictly speaking, they should indicate that time is measured in seconds, so 10 mins -> t = 600.

 

[CrashOveride]

oh ok see coz the actual question only had after 10sec...but i was just trying to think what would happen if it had also said 10min. So from waht i gather from your post, if that event did occur they would have to indicate t as time in seconds. If they didn't, it wouldn't be possible to do it? Just wanted to clear that up.

Yeah for the second thing i was just wondering coz if they hadnt have said "remembering......." you couldnt really do it. I would have preferred if they had said "given v=0 initally" or object starts from rest etc etc.

Oh ok, i didnt do any substituting for the 1st one lol i just expected it to turn out like the original when differentitating. I;ll get onto it. Thanks for your reply.