Use exponent properties to transform exponential expressions and interpret growth/decay rates.
Find the multiplicative factor over a stated time interval from an exponential model
Problem
In \(P(t)=100(1.02)^{12t}\), where \(t\) is years, what is the multiplicative factor over one year?
Big Picture
What this problem is really about
The one-year multiplier must include every base interval contained in a year. We’ll interpret the exponent’s interval count, compare the model at the start and after one year, and divide those outputs so the initial coefficient cancels and leaves only the accumulated factor.
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