World Population Projections

Category: Algebra

"Published in Suisun City, California, USA"

The population of the world in 1995 was 5.7 billion, and the estimated relative growth rate is 2% per year. If the population continues to grow at this rate, when will it reach 57 billion?

Solution:

The word problem is about the exponential growth for a population. The exponential growth is given by the formula

                                      y = x e^rt

where

     y = population at time t
     x = initial size of population
     r = relative rate of growth (expressed as a proportion of the population)
     t = time of growth

Now, refer to the given problem that the initial population is 5.7 billion, the growth rate is 2% per year, and the final population is 57 billion. Substitute the given values to the above equation to solve for time t, we have

                                       y = x e^rt

                                     57 = 5.7 e^0.02t

                                     10 = e^0.02t

                                 ln 10 = ln e^0.02t

                                 0.02t = ln 10

                                       t = 115.129 years

Therefore, the population will reach 57 billion in approximately 115 years, that is, in the year 1995 + 115 = 2110.