5.98 A certain type of bacteria cell divides at a constant rate  over time. (That is, the probability that a cell will divide in a small interval of time t is approximately t.) Given that a population starts out at time zero with k cells of this type and that cell divisions are independent of one another, the size of the population at time t, Y(t), has the probability distribution a Find the expected value of Y(t) in terms of 

and t.

b If, for a certain type of bacteria cell,   0.1 per second and the population starts out with two cells at time zero, find the expected population size after 5 seconds.