Question

The cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years. Use the formula r=(FP)1/n−1 to find the annual inflation rate r to the nearest tenth of a percent, where n is the number of years during which the value increases from P to F. The rate is about %.

Answer 1

Answer:

The inflation rate of increase is 9.22 %

Step-by-step explanation:

Given as :

The initial cost of gas = i = $1.46

The final cost of gas after 10 years = f = $3.53

The time period for increase = n = 10 years

Let The inflation rate of increase = r %

Now, According to question

Inflation rate = [ $(\dfrac{final value}{initial value})^{\frac{1}{time}}$ - 1 ] × 100

Or, r = [ $(\dfrac{f}{i})^{\frac{1}{n}}$ - 1 ] × 100

Or, r = [ $(\dfrac{3.53}{1.46})^{\frac{1}{10}}$ - 1 ] × 100

Or, r = $(2.417)^{\frac{1}{10}}$ - 1 ] × 100

Or, r = [ 1.0922 - 1 ] × 100

∴ r = 0.0922 × 100

i.e r = 9.22 %

So,The inflation rate of increase = r = 9.22 %

Hence, The inflation rate of increase is 9.22 %  Answer