hi i need help for a math question. The question is about geometric sequence, it asking about " in 2004, the turbines generated 326 MW of wind energy, and it is projected that the amount will be 10,000 MW per year by 2010. If this growth were modeled by geometric sequence, determined the value of the annual growth rate from 2004 to 2010."

Question

so far how i did it is:
2004-2010= 6 year difference then
10,000/6 =1666.666 and then 1666.666/326= 5.11
But the answer at the back of my text book say "1.77" i don't know where i am going wrong.. please help

Answer 1

let the rate of growth be r
then 326(1+r)^6 = 10,000
(1+r)^6 = 30.6748.. ( I stored it in memory for accuracy)
take 6th root of both sides
1+r = 30.6748^(1/6) = 1.76928...

or , using GS

a = 326
r = ?

2004 ---> term 1 = a
2010 ----> term 7 = ar^6
326 r^6 = 10000
r^6 = 10000/326 = 30.6748..
same as above
r = 30.6748..^(1/6) = 1.76928... <---- growth factor

Answer 2

When you divide by 10000/6 that's would be the avg rate of climb per year. Your not looking for that. You need to find the geometric sequence for the number 326 to 10k with a annual growth rate of 6 years. You do this by taking 1.77,your given answer, and multiplying 326 by 1.77 6 times. 326x1.77^6 which will roughly equal out to 10k MW.