7. Water is flowing into a large container and is leaking from a hole at the base of the container. At time \(t\) seconds after the water starts to flow, the volume, \(V \mathrm {~cm} ^ { 3 }\), of water in the container is modelled by the differential equation $$\frac { \mathrm { d } V } { \mathrm {~d} t } = 300 - k V$$ where \(k\) is a constant.

1. Solve the differential equation to show that, according to the model, $$V = \frac { 300 } { k } + A \mathrm { e } ^ { - k t }$$ where \(A\) is a constant.
   (5) Given that the container is initially empty and that when \(t = 10\), the volume of water is increasing at a rate of \(200 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\)
2. find the exact value of \(k\).
3. Hence find, according to the model, the time taken for the volume of water in the container to reach 6 litres. Give your answer to the nearest second.