The consumer price index (CPI) for a given year is the...

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 2009 , the CPI was $211 .$ Write a formula for the CPI as a function of $t$ years after $2009,$ assuming that the CPI increases by $2.8 \%$ every year.

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Key Concepts

Exponential Growth

Exponential growth describes a process in which a quantity increases by a fixed percentage over regular time intervals. This type of growth results in a function of the form a(t) = a(0) * (1 + r)^t, where a(0) is the initial value, r is the growth rate expressed as a decimal, and t represents time. The concept is foundational in many fields including economics, biology, and physics.

Annual Percentage Increase

An annual percentage increase means that the quantity grows by a fixed percentage each year. This rate of growth is compounded, so each year's growth builds upon the previous year's value. As a result, even small annual increases can lead to significant changes over time.

Initial Value in Growth Models

The initial value is the starting point of a growth model and serves as the baseline for all future calculations. In exponential growth, this value is crucial because it is multiplied by the compounded growth factor over time, determining the trajectory of the model's progression.

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