A gardener is filling an ornamental pool with water using a hose that delivers 30 litres of water per minute. Initially, the pool is empty. At time t minutes after filling begins, the volume of water in the pool is V litres. The pool has a small leak and loses water at a rate of \(0.01V\) litres per minute.

The differential equation satisfied by V and t is of the form

\[ \frac{dV}{dt} = a - bV \]

(a) Write down the values of the constants a and b.

(b) Solve the differential equation and find the value of t when \(V = 1000\).

(c) Obtain an expression for \(V\) in terms of \(t\) and hence state what happens to \(V\) as \(t\) becomes large.