In this project, you will study various models of a fishery including effects from fishing by humans. LetP(n) represent the total mass of mature Pacific halibut in units of 10⁶kg. We will model the wild halibut biomasswithout any fishingby the following logistic difference equation:

P(n+1)=(1.71)P(n) - (0.00875) (P(n+1))²

Here,r=0.71 andr/M=0.00875

1. (i) (C)Suppose the halibut stock started out at 95% of the carrying capacity according to the model above. But in one massive fishing effort, the halibut biomass is reduced all the way down to 1,000,000 kg (say all within one year). If no further fishing is allowed until stocks recover to 95% of the carrying capacity, how long will that take according to the model? Estimate (to the nearest year) by creating a series of P(n) for years n=1,2,3,... and see which year exceeds 95% of M.