The student population of a certain college was 15,000 in 2010 and has increased 2.3% annually, so that the population t years after 2010 is given by P(t) = 15, 000e 0.023t . (a) How long will it take for the population to reach 20,000? (b) Find the average student population from 2011 to 2013. (c) Find the average rate of growth of the student population from 2015 to 2021. (d) At what rate was population increasing in 2013? (e) Sketch a rough graph of the function and explain what parts b) and c) represent on the graph.