I have found the following question about growth population models.
Let us consider the following situtation:
In a certain habitat we have two populations: birds and worms. It is known that the growth of worms population, in absence of birds, is modeled by the diferential equation: $$w'(t)=0.3w\left(1-\frac{w}{1000}\right).$$ Now, if worms are hunted by birds following a rate (r=0.1) which is proportional to number of worms:
a) Modify the initial equation to collect this phenomenon.
b) Under the above conditions, suggest a modification of the equation, having in count that birds stop hunting when the number of hunted worms is equal to $275$.
My attempt
a)I think that it can be a good idea consider $$w'(t)=0.3w\left(1-\frac{w}{1000}\right)-0.1w(t).$$ b)This is the part where I found a bigger problem. I don't know exactly how to include a term which describes this phenomenon. Could someone help me?