Given plenty of food and space, a particular bug species will reproduce geometrically, with each pair hatching 24 young at age 5 days. (Assume that half the newborn bugs are male and half female, and are ready to reproduce in five days. Also assume each female bug can only reproduce once.) Initially, there are 12 bugs, half male and half female.
a. How many bugs are born on the 5th day? On the 10th day? On the 15th day? On the 35th day?
b. Write a recursive formula for the sequence in 3a.
c. Write an explicit formula for the sequence in 3a.
d. Find the total number of bugs after 60 days.