Rewrite an exponential expression to reveal the repeated growth factor or constant multiplier
Problem
Rewrite \(A~=~100(1.05)^{12t}\), with \(t\) in years, to reveal the annual growth factor. State that factor.
Big Picture
What this problem is really about
A growth factor must match one unit of the model’s input. When the base acts monthly but the input counts years, group one year’s worth of monthly multipliers into a single power, then use the power rule to make that grouped quantity the base raised to t. Repeated growth combines factors by multiplication, not by multiplying the base itself by the number of periods.
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