In 2009 the world population was 68 billion people The expon

In 2009, the world population was 6.8 billion people. The exponential growth rate was 1.13% per year. Find the following:

a) Find the exponential growth function
b) Estimate the population of the world in 2012 and 2020
c) When will the world population be 8 billion people

Solution

a)    The formula for growth of World population is P = P_o e^rt where P₀ is the initial population, r is the growth rate in decimals and t is time in years.

b)    The population of the world in 2012 will be ( 6.8)e^3*0.0113 = 6.8e^0.0339 = (6.8)*(1.0345) = 7.03 billion (approximately).The population of the world in 2020 will be ( 6.8)e^11*0.0113 = ( 6.8)e^0.1243 = ( 6.8)* 1.13236 = 7.70 billion (approximately).

c) Let the World population be 8 billion t years after 2009. Then 8 = ( 6.8)e^0.0113t or, e^0.0113t = 8/6.8 = 1.1765 (approximately). On taking natural logarithms of both the sides, we have ln 1.1765 = 0.0113t ( as ln e = 1) or, 0.0113 t = 0.16254 ( approx.) Therefore, t = 0.16254/0.0113 = 14.38. Thus the World population will be 8 billion in 2009 + 14.38 i.e. in 2024