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?

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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