The Australian Lord Howe Island stick insects may be the rarest insects not already

extinct in the world. It is believed there may be only a few of them (less than 30) left in the wild in the

world. In a lastditch effort to expand the population safely, these stick insects are carefully bred and

introduced back into their native habitat on a very careful linear schedule. Assume that a few weeks

ago, 40 of the stick insects ( P0 ) were introduced on Lord Howe Island by scientists into the existing

habitat. If natural processes occur correctly, each week, the population grows following the linear

growth model. 4 weeks later, there were 65 of the stick insects ( P4 ) on the island.

a) Find an explicit formula for the stick insect population PN after N weeks have passed.

b) Following your formula, how long will it take the stick insect population to grow to 300. Give

the answer accurate to 3 decimal places. Show your work very clearly.

c) If the population continues to grow following this linear model, what is the rate of growth?

Explain in words.