Question

A country's population in 1993 was 127 million. In 2000 it was 132 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.

Answer 1

To solve the exponential growth application question we proceed as follows;
suppose the time, t between 1993 to 2000 is such that in 1993, t=0 and in 2000, t=7.
Note theta the population is in millions;
The exponential formula is given by:
f(t)=ae^(kt)
where;
f(t) =current value
a=initial value
k=constant of proportionality
t=time
substituting the values we have in our formula we get:
132=127e^(7k)
132/127=e^(7k)
introducing the natural logs we get:
ln (132/127)=7k
k=[ln(132/127)]/7
k=0.0055
Thus our formula will be:
f(t)=127e^(0.0055t)
The population in 2008 will be:
f(t)=127e^(15*0.0055)=127e^(0.0825)=137.922
Thus the population in 2008 is appropriately 138 million.