anonymous
  • anonymous
In this question... (image coming). What is Water[t] ? Is it the integral of this function, or is it this function?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Im wondering how you approach a problem like this
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anonymous
  • anonymous
ok so water[t]= 21000 E^t / 4.1 + 1.2 E^t
phi
  • phi
it gives the amount of water in the tank as a function of t

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phi
  • phi
it would be the integral of the rate
anonymous
  • anonymous
but it seems to cap out at 210000 ? when I do that
anonymous
  • anonymous
well not quite... but it stops early
welshfella
  • welshfella
my mistake - i misread the question
anonymous
  • anonymous
are you sure that equation is not just the fill rate? The rate of change? and I have to integrate it into a volume?
phi
  • phi
the rate is approaches a limit but \[ W(t)= \int_0^T r(t) \ dt \] where r(t) is your messy expression
phi
  • phi
** W(T)=...
anonymous
  • anonymous
Im not sure if this makes sense.. but I cooked this up in mathematica.. why does it seem to start out at 210000 cu ft?
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anonymous
  • anonymous
should I be using definite integration not indefinite?
anonymous
  • anonymous
nm, I think you answered that already in your post phi
phi
  • phi
there is the initial condition that W(0)= 0 (it is empty at t=0)
anonymous
  • anonymous
integrating from 0 to T with W[0] = 0 .. empty tank.. gotcha
phi
  • phi
and then rename T to t so you have W[t] that you plot as a function of t
anonymous
  • anonymous
I think this look right...
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anonymous
  • anonymous
Thanks Phi
anonymous
  • anonymous
Should be good from here..
phi
  • phi
yes, looks good

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