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Math Help - Evil combination: Chem and Calc & Finding a Function

  1. #1
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    Evil combination: Chem and Calc & Finding a Function

    Hi there,

    Two questions that have done my head in for the past couple of days; mind taking a look?

    Question one

    For the function y = c(e^-at e^-bt)

    With a, b, c, > 0 and t ≥ 0, find

    i) y (0)
    ii)the limit of y as t approaches infinity
    iii)the point at which y reaches a maximum

    Question two

    In water and in solution the product of the concentrations of hydronium ions, [H3O+] and of hydroxyl ions, [OH-] is very close to 10^-14 (in moles).

    Let S = [H3O+] + [OH-]

    Determine the value of [H3O+] which minimises S.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Wildharmony View Post
    Hi there,

    Question one

    For the function y = c(e^-at e^-bt)

    With a, b, c, > 0 and t ≥ 0, find

    i) y (0)
    ii)the limit of y as t approaches infinity
    iii)the point at which y reaches a maximum
    i)
    \begin{aligned}f(0)&=c\left(e^{-a(0)}-e^{-b(0)}\right)\\<br />
&=c\left(1-1\right)\\<br />
&=0<br />
\end{aligned}

    ii)
    If \lim_{t\to\infty}c\left(e^{-at}-e^{-bt}\right)=0

    iii) f'(t)=c\left(-ae^{-at}+be^{-bt}\right)

    Can you go from there?
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  3. #3
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    I believe i can; thankyou kindly =)
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