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=(p2/p1)^(1/n) -1. The average price of a loaf of bread increased from $0.40 in 1970 to $3.20 in 2013. What was the annual rate of inflation r? Write your answer in decimal form to the nearest hundredth.

r=

Answer 1

Answer: 0.05 ( Approx) is the annual rate of inflation.

Explanation:

Here, the annual rate of inflation r (in decimal form) is given by
`r=(p_2/p_1)^(1/n) -1`

The average price of a loaf of bread increased from $0.40 in 1970 to $3.20 in 2013.

Therefore,
`p_2=3.20` and
`p_1=0.40` and n=43 years

Thus, The required rate of inflation,

`r=(3.20/0.40)^(1/43) -1`

⇒
`r=(8)^(1/43) -1`

⇒
`r=1.04954748605-1`=0.04954748605≈0.05