Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Construct an exponential model from percent growth
Problem
Construct the exponential function for a \(500~\text{dollar}\) investment that grows by \(6\%~\text{each}~\text{year}\).
Big Picture
What this problem is really about
Percent growth repeatedly multiplies the entire current amount, so the exponential base must include the retained whole as well as the increase. We’ll use the starting investment as the coefficient, convert the percent to a decimal, and add it to one to form the yearly factor. Zero-year and one-year checks will verify the initial amount and the stated proportional growth.
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