The number of bags of beetles sold by this company can be approximated by the function S(t)=22000/1+439e^-1.76t where S is the total number of bags sold and t is the number of months since the company began selling.
Problem 1: Find and interpret the rate of change of sales at 5 months.
Problem 2: In what month is the rate of change of sales the largest? Why might this information be useful to the company? Give at least two reasons.
Problem 3: What is the long-term behavior of sales of ladybugs? That is, as time goes on, what is happening to the total sales of ladybugs? What is happening to the rate at which the bugs are being sold? Should the company continue to sell ladybugs? Why or why not?