Users arrive at a nature park in cars according to a Poisson process at a rate of 40 cars per hour. They stay in the park for a random amount of time that is exponentially distributed with mean 3 hours and leave. Assuming the parking lot is sufficiently big so that nobody is turned away, model this situation as a queueing system. Construct the system of differential equations, and hence derive the steady-state probability mass function of the number of cars in the parking lot. Also compute the expected number of cars in the lot in the long run.