The growth of populations of organisms has many engineering and scientific applications. O...

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:

  (P20.4.1)

where kg = the growth rate. The world population in millions from 1950 through 2000 was

(a) Assuming that Eq. (P20.4.1) holds, 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.