The problem
I would appreciate if you could help me with following math..: Please use exponential growth model y=Ae^kt to answer.:
The population of Whereville was 742 in 1970 and 1124 in 2010. What would have been the population in 1990?
Answer provided by our tutors
The best approach to this, without using expensive mathematics,...
we adjust the original equation so that 'k' can be simply solved for and we also normalize the years to 1970, so '1970' is '0', '2010' is '40' and '1990' is '20
to solve for 'k' we need a simpler approach:
y=Ae^(kt)
y/A=e^(kt)
ln(y/A)=ln(e^kt))
ln(y/A)=kt
and now we can solve for 'k', given y=1124 (population in 2010), A=742 (original population, 1970) and t=40 (40 years from 1970 to 2010):
k=ln(y/A)/t
k=0.0103824948
Now that 'k' is known, we have a more simple equation to solve for 'y':
y=742e^(0.0103824948*20)
y=913.24
So the population in 1990 would have been approximately 913