1. The population of a certain species of insects in a nearby farm increases exponentially according to the model, () = 2580^0.124where P is the number of insects and t is the time in weeks since the original colony settled in the farm.
   1. [3 pts]Find the number of insects in the original colony that settled in the farm. Please show your work.
2. [2 pts]Find the rate of increase of the insect population for each week that passed by. Please show your work.
3. [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. Please show your work.
4. [5 pts] How long will it take for the population to reach 9000? Please show your work.