Recognize constant percent growth or decay as evidence for an exponential model.
Interpret the base of an exponential model
Problem
Interpret \(f(x)~=~300\cdot~1.12^{x}\). State the base, retained and growth percentages, recurrence, \(\text{first}~\text{two}\) values, and \(\text{three}\text{-}\text{step}\) factor and percent change.
Big Picture
What this problem is really about
The base of an exponential model carries both a retained percentage and a one-step percent change. We’ll separate the whole from the excess above one, express the model as a recurrence, and calculate early values. For several intervals, we’ll raise the base to a power before converting the cumulative factor into cumulative percent growth, preserving compounding.
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