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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.

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Answer:

the annual rate of inflation r is 0.023

Step-by-step explanation:

Given by the expression:

[tex]r=(\frac{p_2}{p_1})^{1/n}-1[/tex]

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

Let [tex]p_1 = 0.36[/tex]

[tex]p_2 = 3.53[/tex]

n = 2013 - 1913 = 100

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

[tex]r=(\frac{3.53}{0.36})^{1/100}-1[/tex]

r = 0.023

Hence, the annual rate of inflation r is 0.023

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