MAT 117 - Summer 2022 NAME: Unit D Problem Set 2 . The population of a certain species of insects in a nearby farm increases exponentially according to the model, P(t) = 2580e 0.124t where P is the number of insects and t is the time in weeks since the original colony settled in the farm. A. [3 pts] Find the number of insects in the original colony that settled in the farm. B. [2 pts] Find the rate of increase of the insect population for each week that passed by. C. [4 pts] How many insects would you expect to be in the colony after 16 weeks if the population growth follows the model? Round off to the nearest whole number. D. [5 pts] How long will it take for the population to reach 9000