Apparently you're having some problems with this.

(i) If you write it as:

Then the rate at which the weight is changing is dependent on an exponentially decaying factor of the current weight right? As time proceeds, the rate at which the weight is changing must continually decrease because of this exponential factor. But that factor never goes to zero so I'd expect the weight to asymptotically approach some limiting value.

(ii) When you separate variables and integrate you'll get:

You can do that right? Integrate it and obtain the function then try and do the rest.