The population of a town is 500. Then the population decreases by 100 over the year, and the population grows by 100 over the next year. What is the average yearly growth rate in the population over the two-year period? Does this growth rate fully represent what happened over this period? If not, what calculations would you make to give a better representation?

Answer:

Average Annual Growth Rate (AAGR) is given by:

AAGR= (Growth Rate in Year 1 + Growth Rate in Year 2)/2

     Growth Rate in Year 1 = - 100/500 = - 0.20

     Growth Rate in Year 2 = 100/500 = 0.20

Substituting, we get:

AAGR = (-0.2+ 0.2)/2 = 0

So,

the Average Yearly Growth Rate over the two - year period = 0

This Growth Rate does not fully represent what happened over this period.

To give a better representation we have to calculate AAGR using Percentage Growth for each year as follows:

Beginning Population= 500

End of year 1 Population = 400

End of year 2 Population = 500

The Growth Rate of Year 1 = (400/500) -1 = - 0.20 = - 20%

The Growth Rate of Year 2 = (500/400) - 1 = 0.25 = + 25%

AAGR is calculated as the sum of each year's Growth Rate divided by the nuber of years:

AAGR = -20+25/2 = +2.5 %

This value of AAGR = + 2.5 % gives a better representation.