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:

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

(a) Assuming that Eq. (P22.4.1) holds, use the data from 1950 through 1970 to estimate k_g.
(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.

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dp = kg p dt