Asked by Anonymous
The population of the world in 1987 was 5 billion and the annual growth rate was
estimated at 2 percent per year. Assuming that the world population follows an
exponential growth model, find the projected world population in 2015.
estimated at 2 percent per year. Assuming that the world population follows an
exponential growth model, find the projected world population in 2015.
Answers
Answered by
MathMate
Assume formula
Population in billions at time t (counting from 1987) as
P(t)=Ae^(kt)
where A and k are constants.
At t=0 (1987),
P(0)=Ae^(0)=A=5
the formula becomes:
P(t)=5e^(kt)
P(1)=5*1.02=5e^(kt) [t=1]
=>
e^(k)=1.02 [t=1]
Take log both sides
k=log(1.02) [natural log]
So
P(t)=5e^(t*log(1.02))
where log(1.02)=0.0198 approx.
Population in billions at time t (counting from 1987) as
P(t)=Ae^(kt)
where A and k are constants.
At t=0 (1987),
P(0)=Ae^(0)=A=5
the formula becomes:
P(t)=5e^(kt)
P(1)=5*1.02=5e^(kt) [t=1]
=>
e^(k)=1.02 [t=1]
Take log both sides
k=log(1.02) [natural log]
So
P(t)=5e^(t*log(1.02))
where log(1.02)=0.0198 approx.
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