The population of world was around 6.1 billion in year 2000. Birth rate around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let us assume that carrying capacity for world population is 20 billion. (a) Write logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of initial relative growth rate.) (b) Use the logistic model to estimate the world population in the year 2010 and compare with actual population of 6.9 billion. (c) Use the logistic model to predict the world population in the years 2100 and 2500