The oil reservoir of the Magic Kristin Engine has sprung a leak and the hole is slowly increasing in size so that oil leaks out at a rate of $r\left(t\right) = 0.2\left(1.2\right)^{t}$ liters/minute of oil after $t$ minutes. If $50$ liters of oil in the engine all spurts out, the engine will be ruined. Jeremy locates the leak in $20$ minutes and shuts down the engine. Decide if he was in time.