Question

When the average price of an item increases from p1 to p2 over a period of n years, the annual rate of inflation r (in decimal form) is given by r=(p2p1)1/n−1. The average price of a gallon of milk increased from $0.36 in 1913 to $3.53 in 2013. What was the annual rate of inflation r? Write your answer in decimal form to the nearest thousandth.

Answer 1

the annual rate of inflation r is 0.023

Explanation:

Given by the expression:

`r=((p_2)/(p_1))^(1/n)-1`

The average price of a gallon of milk increased from $0.36 in 1913 to $3.53 in 2013.

Let
`p_1 = 0.36`

`p_2 = 3.53`

n = 2013 - 1913 = 100

replacing our values into the given equation; then the annual rate of inflation r is as follows:

`r=((3.53)/(0.36))^(1/100)-1`

r = 0.023

Hence, the annual rate of inflation r is 0.023