Question 1114522: A man gets a rise of 10% in salary at the end of his first year of service, and further rises of 20% and 25% at the end of the second and third years respectively,the rise in each case being calculated on his salary at the beginning of the year. Find geometric mean.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it's been a while, so i forgot what a geometric mean is.
fortunately there are references on the web that can help.
here's one.
http://www.mathsisfun.com/numbers/geometric-mean.html
based on your description of the problem, you have a series of numbers.
if the first number is x, then:
the second number is 1.1 * x.
the third number is 1.2 * 1.1 * x.
the fourth number is 1.25 * 1.2 * 1.1 * x
this is based on my understanding that each year's increase is based on the salary at the beginning of that year.
the geometric means would therefore be:
the fourth root of (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)
this becomes the fourth foot of (1.1^3 * 1.2^2 * 1.25 * x^4).
this becomes equal to the fourth root of (1.1^3 * 1.2^2 * 1.25) * x.
this becomes equal to the fourth root of (2.3958) * x.
this becomes equal to 1.244121056 * x
if this is true, then (1.244121056 * x) ^ 4 must be equal to (x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x)
(1.244121056 * x) ^ 4 is equal to 2.3958 * x^4.
(x * 1.1 * x * 1.2 * 1.1 * x * 1.25 * 1.2 * 1.1 * x) is equal to 2.3958 * x^4.
this confirms that the geometric mean has been calculated correctly according to the instructions provided by the referenced website.
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