Build a function from context by determining an explicit formula, recursive rule, or calculation process.
Build an explicit exponential function from percent growth
Problem
A population starts at \(500\) and grows by \(8\%\) each year. Write an explicit exponential function for the population.
Big Picture
What this problem is really about
Percent growth is multiplicative because each period’s change is based on the current amount. We’ll define elapsed time and the changing population, use the time-zero amount as the leading factor, and convert the growth percent into a full one-period multiplier. Raising that multiplier to the number of periods accounts for repeated growth, while zero- and one-period checks verify the model.
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