A country's population in 1995 was 164 million. In 2001 it was 169 million. How do you estimate the population in 2015 using exponential growth formula?

Question

4005 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-23T21:00:31

#181.268 # million to 3 dp

#color(blue)("Initial condition")#

The difference in years from 1995 to 2001 is 6 years
The change in population count in millions was 164 to 169

Let the unknown growth percentage be #x%# giving:

#164(1+x/100)^6=169#

#((100+x)/100)^6=169/164#

Taking logs

#6ln(100+x)-6ln(100)=ln(169)-ln(164)#

#ln(100+x)=(ln(169)-ln(164))/6+ln(100)#

Set #y=100+x# giving

#ln(y)~~ 4.610175....#

#=>e^(4.610175...) ~~ y#
#=>y~~100.501792...#

Thus #x~~0.501792...#
~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("New condition")#

Time span from #t_o=2015-1995= 20# years

Thus population estimate at 2015 is:

#164((100.501792..)/100)^20~~181.268 # million to 3 dp