(a)[1]
Give the values of the constants $a$ and $b$.
(b)[6]
Solve the differential equation, then determine the value of $t$ when $V = 1000$.
(c)[2]
Find an expression for $V$ in terms of $t$ and therefore state how $V$ behaves as $t$ becomes large.
Mathematics 9709 · AS & A Level · Differential equations
Differential equations — practice question
A gardener is topping up an ornamental pool with water by means of a hose that supplies $30$ litres each minute. The pool starts off empty. If $t$ minutes have passed since the filling began, the amount of water in the pool is $V$ litres. There is a small leak in the pool, so water escapes at a rate of $0.01V$ litres per minute. The differential equation relating $V$ and $t$ has the form $\frac{dV}{dt} = a - bV$.