SOLUTION: i am to find the average annual rate of inflation...the cost of box of cereal increased from 4.25 to 5.5 over 5 years. i believe i should be solving using final amount 5.5=initial

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Question 393060: i am to find the average annual rate of inflation...the cost of box of cereal increased from 4.25 to 5.5 over 5 years. i believe i should be solving using final amount 5.5=initial amount 4.25(1+rate of change) to the nth power or in this case the power of 5. i get 75% and that doesn't make sense.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Your equation is good:
5.5+=+4.25%2A%281%2Bp%29%5E5
So your solution must have an error.

To solve the equation we should start by isolating the base and its exponent. Dividing both sides by 4.25 we get:
5.5%2F4.25+=+%281%2Bp%29%5E5
Next we want to change the exponent from a 5 to a 1. The way to do this is to raise both sides of the equation to the reciprocal of 5 power:
%285.5%2F4.25%29%5E%281%2F5%29+=+%28%281%2Bp%29%5E5%29%5E%281%2F5%29
On the right side, since the rule for raising a power to a power is to multiply the exponents and since the product of reciprocals is always a 1, we get the desired exponent of 1. (This is why we use reciprocals to change exponents into a 1.) Now the equation is:
%285.5%2F4.25%29%5E%281%2F5%29+=+1%2Bp
Subtracting 1 from each side we get:
%285.5%2F4.25%29%5E%281%2F5%29+-+1++=+p
This is an exact expression for the decimal version of the average annual rate of inflation. If you want the actual percent number, we would just multiply by 100: 100%28%285.5%2F4.25%29%5E%281%2F5%29+-+1%29.

If you want a decimal approximation, get out your calculator (or use the calculator program that is found on most computers). Use the "^" button to raise to a power. If the calculator has buttons for parentheses then you just type in exactly what you see, using the "^" in front of the %281%2F5%29. If not, then divide the fraction to convert it into a decimal and then raise that to the 0.2 (1/5 = 0.2) power. (You should get approximately 0.053 or 5.3%)