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.

Step-by-step 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