The growth of populations of organisms has many engineering and scientific applications. One of the simplest models assumes that the rate of change of the population p is proportional to the existing population at any time t:dp/dt = kgPwhere kg: the growth rate. The world population in millions from 1950 through 2000 was t 1950 1955 1960 1965 1970 1975p 2554 2780 3040 3346 3708 4087t 1980 1985 1990 1995 2000p 4454 4850 5276 5686 6079Requried:a. Use the data from 1950 through 1970 to estimate kg. b. Use the fourth-order RK method along with the results of (a) to stimulate the world population from 1950 to 2050 with a step size of 5 years. Display your simulation results along with the data on a plot.