A country's population in 1994 was 195 million. In 2002 it was 199 million. How do you estimate the population in 2016 using the exponential growth formula?

1 Answer
Shwetank Mauria
Mar 7, 2016

Population in 2016 is estimated to be #206.20# million

Explanation:

Let the population in starting year be #P_0# and #g# be the exponential growth. Then the population #P_n# in #n^th# will be given by #P_n=P_0xx(1+g)^n#.

As the population in 1994 was 195 million and in 2002 (after 8 years), it was 199 million. We have

#199=195xx(1+g)^8# or #(1+g)^8=199/195#.

Taking log, #8xxlog(1+g)=log199-log195=0.0088185# or

#log(1+g)=0.0011022# or #1+g=1.002541# or #g=0.002541# i.e.

Growth rate is #0.2541%#.

The population in 2016 (after 22 years) would be

#195xx(1+g)^22# or #195xx1.002541^22=195xx1.0574279=206.20# million.

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