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 th world. In a last-ditch 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 75 of the stick insects (P4 ) on the island. a) Find an explicit formula for the stick insect population Py after N weeks have passed. b) Following your formula, how long will it take the stick insect population to grow to 350. Give the answer accurate to 3 decimal places. c) If the population continues to grow following this linear model, what is the rate of growth? Explain in words what this means.