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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.

Respuesta :

irspow
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:

Population in 2016 = 184 million

Step-by-step explanation:

Exponential growth of a country's population will be represented by [tex]P=P_{0}(r)^{t}[/tex]

Where P = Current population

P0 = initial population

r = rate of growth

t = time period

Now population in 1996

[tex]162=156(r)^{6}[/tex]

[tex]r^{6}=162/156=1.038[/tex]

[tex]r=(1.038)^{\frac{1}{6}} = 1.006[/tex]

Now population in year 2016

[tex]P=156(1.006)^{26}=156(1.176)=184[/tex]

Therefore the population in 2016 will be 184 million.

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