Question

A country's population in 1993 was 171 million. In 1999 it was 176 million. Estimate the population in 2012 using the exponential growth formula. Round your answer to the nearest million.

Answer 1

This is the concept of application of an exponential growth functions. This question can be modeled using the exponential formula;
f(t)=ae^(kt)
where;
a=initial population
f(x)=current population
t=time
k=constant of proportionality
suppose the time at 1993 is t=0 and time in 1999 is t= 6
N/B. The population is in millions;
Thus;
176=171e^(6t)
176/171=e^(6t)
introducing the natural logs we getL
6t=ln(176/171)
t=1/6ln(176/171)
t=0.0048
Hence;
f(t)=171e^(0.0048t)
Therefore the population in 2012 will be:
t=19
thus;
f(t)=171e^(0.0048*19)
f(t)=187.33
Thus, the population will be given by:
f(t)=187 million