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
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:
However, the solution to the problem given in the back of the book is like so:
Edit: super stupid moment
I forgot that