Use exponent properties to interpret exponential expressions, including percent growth and decay.
Rewrite an exponential model so the input uses a different time unit
Problem
Rewrite \(P(m)=100(1.01)^m\) using elapsed years \(y\) instead of months \(m\). Substitute \(m=12y\), apply \(a^{12y}=(a^12)^y\), and identify the \(\text{one}\text{-}\text{year}\) growth multiplier while preserving the initial value.
Big Picture
What this problem is really about
Changing an exponential model’s time unit changes how many old intervals the exponent counts, while preserving the same function. We’ll convert the new time variable into old intervals, substitute that exponent, and regroup with the power-of-a-power rule to expose the new interval multiplier.
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