Answer:
11%
Explanation:
You want to know the rate of inflation if the price of a haircut increased from $7 to $20 in 10 years.
Inflation
The inflation of prices is modeled by an exponential function.
p(t) = p₀·(1 +r)^t
where p₀ in the price at t=0, r is the annual inflation rate, and t is the number of years.
Solving for r, we find ...
p(t)/p₀ = (1 +r)^t . . . . . . . . divide by p₀
(p(t)/p₀)^(1/t) = 1 +r . . . . . . take the t-th root
r = (p(t)/p₀)^(1/t) -1 . . . . . . . subtract 1
For the given numbers, we find the rate to be ...
r = (20/7)^(1/10) -1 ≈ 0.11 = 11%
The rate of inflation is 11% per year.
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