f(x)=424,644(1.01866)^x

Question

need to find what year the population of Atlanta will be doubled using the function f(x)=424,644(1.01866)^x, but put that into a logarithm like 2010+the logarithm

Answer 1

The growth rate is 1.01866ˣ. When the growth rate is doubled this expression=2.

xlog(1.01866)=log(2) so x=log(2)/log(1.01866)=37.4917 approx.

So it will take about 37.5 years for the population to double.

If the start year was 2010 then by 2047 the population is predicted to double.

The expression is 2010+log(2)/log(1.01866).