The world’s population in 1990 was about 5 billion, and data show that birth rates range from 35 to 40 per thousand per year and death rates from 15 to 20. Take this to imply a net annual growth rate of 20 per thousand. One model for world population assumes constant per capita growth, with a per capita growth rate of 20/1000 = 0.02. a) Write a differential equation for P that expresses this assumption. Use P to denote the world population, measured in billions. b) According to the differential equation in (a), at what rate (in billions of persons per year) was the world population growing in 1990? c) By applying Euler’s method to this model, using the initial value of 5 billion in 1990, estimate the world population in the years 1980, 2000, 2040, and 2230. Present a table of successive approximations that stabilizes with one decimal place of accuracy (in billions). What step size did you have to use to obtain this accuracy?