6. Liquid is poured into a container at a constant rate of \(30 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\). At time \(t\) seconds liquid is leaking from the container at a rate of \(\frac { 2 } { 15 } V \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\), where \(V \mathrm {~cm} ^ { 3 }\) is the volume of liquid in the container at that time.

1. Show that $$- 15 \frac { \mathrm {~d} V } { \mathrm {~d} t } = 2 V - 450$$ Given that \(V = 1000\) when \(t = 0\),
2. find the solution of the differential equation, in the form \(V = \mathrm { f } ( t )\).
3. Find the limiting value of \(V\) as \(t \rightarrow \infty\).