Question

The number of new domestic wind turbine generators installed each year in a particular country has been forecast to increase at a constant multiplicative rate of 15% per annum for the foreseeable future. This year (t = 0) 100 new generators were installed. What is the total number of new generators including this year's, that would have been installed within the next ten years (that is up to and including year t = 9)? Use a discrete model for the growth process.

2030

235

1679

900

Answer 1

Here at the “period 0” the initial numbers of generators were “100” and the growth rate if 15% per annum. So, the numbers of new generators including this year within the next 10 years is given by, => 100*1.15^9 = 351.79 = 352. SO, the numbers of new generator is given by “352”.

Answer 2

[(100*15%)*9]+100=235

Answer 3

Use the sum of a geometric series

100[(1-1.15^9+1)/(1-1.15)] = 2,030

This is a sum of all the generators created over the timeframe. So 100 in the first year plus 115 in year 2 etc....