In 2000, the percentage of the population living in urban areas was 73 and this percentage decreased by 2.4 each year, on average, in the period 2000 - 2010.

Question

In 2000, the percentage of the population living in the suburbs was 4 and this percentage increased by 2.4 each year, on average, in the period 2000 - 2010. Assuming this trend continues, estimate the year in which the percentage of the population living in urban areas will be equal to the percentage living in the suburbs.

Answer 1

I was asked to answer your question, but the The growth is exponential by year, so we have the following equation:

.73(1 - .24)^x = .04(1+.24)^x

Put the constants to one side and the exponential terms to the other:

(.76^x)/(1.24)^x = .04/.73

=> (.76/1.24)^x = .04/.73

=> (.6129)^x = .04/.73

=> log base .6129 of .6129^x = log base .6129 of (.04/.73)

=> x = log base .6129 of (.04/.73) then perform a change of base to base e, for the natural log ...ln:

=> x = (ln(.04/.73))/ln(.6129))

=> x = 5.94 So, in the fifth year, just before the sixth year, we see there are equal percentages of living in urban areas and suburban areas. You can go back and check for x = 5.94 (rounded), and the percent is a bit over 14%... it checks out. :-)