# Thread: Tub Leaking Problem

1. ## Tub Leaking Problem

This is a question from my ODE class so I assume it's ok to post here

the problem is
A 200 gallon tank, initially full of water, develops a leak at the bottom. Given that 20% of the water leaks out in the ﬁrst 4 minutes, ﬁnd the amount of water left in the tank t minutes
after the leak develops if:
(i) The water drains oﬀ a rate proportional to the amount of water present.
(ii) The water drains oﬀ a rate proportional to the product of the time elapsed and the
amount of water present.
(iii) The water drains oﬀ a rate proportional to the square root of the amount of water
present.

I really only need help with the first one so I can get an idea of what I'm supposed to do.
I went through the whole hoopla of integrating etc. etc. and got this:

$\displaystyle V(t) = 200e^{ln(.8)t/4}$

However, the solution to the problem given in the back of the book is like so:

$\displaystyle V(t) = 200(4/5)^{t/4}$

Edit: super stupid moment
I forgot that $\displaystyle e^{ln(.8)}=4/5$
epic facepalm

2. What DE did you use to model (i)?