If the inflation rate is 3.5 % per year and the average...

If the inflation rate is $3.5 \%$ per year and the average price of a home is 195,000 dollars, the average price of a home after $n$ years is given by $A_{n}=195,000(1.035)^{n} .$ Find the average price of the home after 6 years.

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Key Concepts

Function Evaluation

Function evaluation involves substituting specific values into a mathematical expression to compute an outcome. In the context of exponential growth due to inflation, evaluating the function for a given number of time periods allows one to calculate the resulting price or value after the compounded growth.

Compound Interest

Compound interest is the idea that interest is earned not just on the initial amount, but also on the accumulated interest from previous periods. This same principle applies to inflation computations, where prices increase by a fixed percentage each period, leading to an exponential effect over time.

Exponential Growth

Exponential growth describes a process where a quantity increases at a rate proportional to its current value, resulting in a rapid rise over time. This concept is essential because it illustrates how even small constant percentage increases, such as an inflation rate, can lead to significant changes when compounded over multiple periods.

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