Each individual in a biological population is assumed to give birth at an exponential rate , and to die at an exponential rate u. In addition, there is an exponential rate of increase due to immigration. However, immi- gration is not allowed when the population size is N or larger.

(a) Set this up as a birth and death model.

(b) If N = 3,10=, u = 2, determine the proportion of time that immigration is restricted.