The consumer price index (CPI) for a given year is the amount of money in that year that has the same purchasing power as $100 in 1983. At the start of 2015, the CPI was 234.1 Write a formula for the CPI as a function of t years after 2015, assuming that the CPI increases by 2.3% every year.

CPI (n) = 234.1 x 1.023ⁿ

Explanation:

Let P be an exponential function of n (time) with a base a:

Consumer price index = P₀ x aⁿ

where

P₀ is the CPI when n = 0, P₀ = 234.1

a = 1 + r (rate of increase) = 1 + 2.3% = 1 + 0.023 = 1.023

the CPI will increase as n increases

CPI (n) = P₀ x aⁿ = 234.1 x 1.023ⁿ

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