Question

In this question... (image coming).
What is Water[t] ? Is it the integral of this function, or is it this function?

Answer 1

Im wondering how you approach a problem like this

Answer 2

ok so water[t]= 21000 E^t / 4.1 + 1.2 E^t

Answer 3

it gives the amount of water in the tank as a function of t

Answer 4

it would be the integral of the rate

Answer 5

but it seems to cap out at 210000 ? when I do that

Answer 6

well not quite... but it stops early

Answer 7

my mistake - i misread the question

Answer 8

are you sure that equation is not just the fill rate? The rate of change? and I have to integrate it into a volume?

Answer 9

the rate is approaches a limit
but
\[ W(t)= \int_0^T r(t) \ dt \]
where r(t) is your messy expression

Answer 10

** W(T)=...

Answer 11

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?

Answer 12

should I be using definite integration not indefinite?

Answer 13

nm, I think you answered that already in your post phi

Answer 14

there is the initial condition that W(0)= 0 (it is empty at t=0)

Answer 15

integrating from 0 to T
with W[0] = 0 .. empty tank..
gotcha

Answer 16

and then rename T to t so you have W[t]
that you plot as a function of t

Answer 17

I think this look right...

Answer 18

Thanks Phi

Answer 19

Should be good from here..

Answer 20

yes, looks good