Rewrite functions in equivalent forms to reveal and explain useful properties.
Rewrite an exponential function to reveal the growth or decay factor for a different time interval
Problem
Rewrite \(100(1.02)^{12t}\), where \(t\) is in years, in the form \(A(b)^t\). State the exact annual growth factor and its decimal approximation.
Big Picture
What this problem is really about
Match the exponential factor to the time unit requested. Regroup the product in the exponent with the power rule so one new base represents all of the smaller compounding intervals within a single larger interval. Preserve that powered base as the exact factor, evaluate it only afterward, and convert the multiplier to a percent change only if that interpretation is useful.
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