please answer question 9. its a multi step question that covers many sections of different chapters. Im having trouble believing that the answers I arrived too are incorrect. Please solve each part throughly with explanations. Also, please do not submit incorrect work that will not help me fix any errors that I may have made. Look forward to growing. Thanks in advance! :)

9. Saving the Kakapo You are modeling the size of the population of kakapo (a rare flightless parrot) in an island reserve in New Zealand. You want to use the mathematical model to predict the size of the population. The data in this question are taken from Elliot et al. (2001) (a) You start by writing a word equation relating the population size N, in year t, that is, t years after the study began, to the pop- ulation size N,+1 in the next year. N.+1=N,+ number of birds - number of birds that born in one year die in one year We will derive together formulas for each of these terms. (i) To estimate the number of birds born, assume that half of the birds are female. A female bird lays one egg every four years. However, because of the large numbers of predators (mostly rats) only 29% of hatchlings survive their first year. Explain how based on this data our prediction for the number of births is N, -0.5.0.25. 0.29 = 0.03625N,. () Kakapo life expectancy is not well understood, but we will assume that they live around 50 years. That is, in a given year, one in fifty kakapo will die. What is the corresponding number of deaths? (iii) Assume that the starting population size on this island is 50 birds (i.e., No = 50). Calculate the predicted population size over the next five years (i.e., calculate Ni, N2, ..., Ns). (iv) When (if ever) will the population size reach 100 birds? What about 200 birds? (You will find it helpful to derive an ex- plicit formula for the size of the population N)