# Evil combination: Chem and Calc & Finding a Function

• Nov 18th 2008, 01:53 PM
Wildharmony
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.
• Nov 18th 2008, 02:01 PM
Mathstud28
Quote:

Originally Posted by Wildharmony
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)\\
&=c\left(1-1\right)\\
&=0
\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?
• Nov 18th 2008, 02:28 PM
Wildharmony
I believe i can; thankyou kindly =)