Question

A country's population in 1990 was 156 million. In 1996 it was 162 million. Estimate the population in 2016 using the exponential growth formula. round to the nearest million.

Answer 1

Exponential growth is of the form:

F=Ir^t, F=final amount, I=initial amount, r=rate, t=time

For this problem we need to find r and we are given two points so:

162/156=(ar^6)/(ar^0)

27/26=r^6

r=(27/26)^(1/6)

F(y)=156(27/26)^(1/6)^(y-1990)

F(2016)=156(27/26)^(1/6)^26

F(2016)=156(27/26)^(13/3)

F(2016)=184 million (to nearest million)

Answer 2

Population in 2016 = 184 million

Explanation:

Exponential growth of a country's population will be represented by
`P=P_(0)(r)^(t)`

Where P = Current population

P0 = initial population

r = rate of growth

t = time period

Now population in 1996

`162=156(r)^(6)`

`r^(6)=162/156=1.038`

`r=(1.038)^{(1)/(6)} = 1.006`

Now population in year 2016

`P=156(1.006)^(26)=156(1.176)=184`

Therefore the population in 2016 will be 184 million.