## Tuesday, December 11, 2012

### 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 ert

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 ert

57 = 5.7 e0.02t

10 = e0.02t

ln 10 = ln e0.02t

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.