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."
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
To find the annual growth rate of a geometric sequence, you need to determine the common ratio between consecutive terms. In this case, the term in 2004 is 326 MW, and the term in 2010 is 10,000 MW.
To find the common ratio, you can use the formula:
Common Ratio = (Value in 2010) / (Value in 2004)
So, in this case, the common ratio is:
Common Ratio = 10,000 / 326 = 30.67 (approximately)
However, it seems that there might be a mistake in your calculation. You divided 10,000 by 6 and then divided that result by 326. This approach does not accurately represent the growth rate over the 6-year period.
To find the annual growth rate, you need to find the nth root of the common ratio, where n is the number of years that have passed.
In this case, the number of years that have passed is 6.
So, the annual growth rate would be:
Annual Growth Rate = (Common Ratio)^(1/n)
Annual Growth Rate = (30.67)^(1/6) = 1.77 (approximately)
Therefore, the correct answer is indeed 1.77.