E: create a recursive function to model the table of values. in that function, the year 2013 is the first data point, so n = 1 for 2013. this means f(1) = 125 is the first term of the sequence, and r is the constant factor by which the number increases every year.

f: rewrite the recursive equation that you got in part e as an explicit equation where the initial value is a and the time elapsed is n years.

year 2013 2014 2015 2016

population of butterflies 125 150 180 216