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    Hi guys,

    I need some help with a differentiation question. I've checked the answer but i cannot figure out how they solved it... =(

    I've uploaded the question and answers to this thread just to make things easy.



    These are the problems i am having:

    part ic) 'after a long time' therefore means t→∞ so e^kt would tend to 0 right? which means p will equal 0 after a long time? but the answer says it will increase to infinity..... =S

    part iia) when they make t= 0, how did they get dp/dt = 6?!

    iib) see, this time p=0 after a long time becase as t→∞, e^(at-bt^2) tends to 0....so why is this wrong for part ic?

    thank you so so so much for helping.
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    'after a long time' therefore means t→∞ so e^kt would tend to 0 right?
    Not sure how you came to that answer. t gets bigger so e^kt gets bigger, seems pretty obvious to me.
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    (Original post by strwbry_short_cake)
    Hi guys,

    I need some help with a differentiation question. I've checked the answer but i cannot figure out how they solved it... =(

    I've uploaded the question and answers to this thread just to make things easy.


    These are the problems i am having:

    part ic) 'after a long time' therefore means t→∞ so e^kt would tend to 0 right?
    no; for t->Inf exp(kt)->Inf

    which means p will equal 0 after a long time? but the answer says it will increase to infinity..... =S



    part iia) when they make t= 0, how did they get dp/dt = 6?!
    P(t)=3*exp(at-bt^2)
    dP/dt=3*(exp(at-bt^2))*(a-2bt)

    at time t=0, dP/dt=3*a

    iib) see, this time p=0 after a long time becase as t→∞, e^(at-bt^2) tends to 0.....
    Because e^(-t)->0 for t->Inf
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    thanks for helping

    o yes, thinking about it, a positive exponential will always increase to infinity while a negative exponential will decrease.....

    but i still don't understand how they got the '6' in the first place:

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    (Original post by strwbry_short_cake)
    thanks for helping

    o yes, thinking about it, a positive exponential will always increase to infinity while a negative exponential will decrease.....

    but i still don't understand how they got the '6' in the first place:
    sorry, I didn't see you had to determine a and b.

    I would do it like this: maximum at t=10 => dP/dt=0 at t=10 , so

    3*(exp(10a-100b))*(a-20b)=0
    i.e.
    (1) a=20b
    and from before you know that
    (2) 3a=6,

    so just solve (1) for b and plug in a=2.

    Oh and the "6" is given in the introduction (i.e. they measured it experimentally). btw is it normal that they don't write down the units?
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    oh i see, i didn't use the dp/dt = 6 because i thought it belonged to the first model...
    yh they sometimes don't write the units in the answers.....
    thanks for the help btw.
 
 
 
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