A population of insects is divided into two stage categories. The females in the first category or stage produce on average 2 female offspring and have a survival rate of 25% to stage 2. The females in stage 2 produce on average 5 female offspring and die after one time period in stage 2.

a. If the population were to exist for a long time with the above-mentioned conditions staying the same, what would the long-term growth rate of the population be per time period? If at time 150 the population of insects had reached the long-term growth rate with 1 million females present, approximately how many females would be present at time 151?

b. The population were to exist for a long time with the above-mentioned conditions staying the same, approximately what fraction of the population would be in each of the two stages?