Recognize constant percent growth or decay as evidence for an exponential model.
Evaluate an exponential model after several intervals
Problem
Find the value after \(3~\text{intervals}\) for \(f(x)=100(1.2)^x\).
Big Picture
What this problem is really about
The exponent counts how many times the interval factor is applied, so several intervals mean repeated multiplication rather than multiplying once by the interval count. We’ll substitute the requested count, evaluate the power first, and then apply the initial value. Iterating the factor step by step provides an independent check.
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