Question 393060
Your equation is good:
{{{5.5 = 4.25*(1+p)^5}}}
So your solution must have an error.<br>
To solve the equation we should start by isolating the base and its exponent. Dividing both sides by 4.25 we get:
{{{5.5/4.25 = (1+p)^5}}}
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:
{{{(5.5/4.25)^(1/5) = ((1+p)^5)^(1/5)}}}
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:
{{{(5.5/4.25)^(1/5) = 1+p}}}
Subtracting 1 from each side we get:
{{{(5.5/4.25)^(1/5) - 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((5.5/4.25)^(1/5) - 1)}}}.<br>
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 {{{(1/5)}}}. 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%)