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

1. anonymous

Im wondering how you approach a problem like this

2. anonymous

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

3. phi

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

4. phi

it would be the integral of the rate

5. anonymous

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

6. anonymous

well not quite... but it stops early

7. welshfella

my mistake - i misread the question

8. 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?

9. phi

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

10. phi

** W(T)=...

11. 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?

12. anonymous

should I be using definite integration not indefinite?

13. anonymous

14. phi

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

15. anonymous

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

16. phi

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

17. anonymous

I think this look right...

18. anonymous

Thanks Phi

19. anonymous

Should be good from here..

20. phi

yes, looks good