Use exponent properties to transform exponential expressions and interpret growth/decay rates.
Rewrite an exponential decay expression in negative-exponent form using \((b^k)^t=b^{kt}\)
Problem
Rewrite \(100(1/2)^t\) using positive base \(2\) and a negative exponent. Show \(1/2=2^{-1}\), multiply the nested exponents, and state the equivalent decay expression.
Big Picture
What this problem is really about
A reciprocal decay base can be expressed as a positive base with a negative exponent. We’ll rewrite the reciprocal using a negative-first power, apply the power-of-a-power rule without losing the sign, keep the outside coefficient unchanged, and verify the decay form at one input.
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