Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve an exponential equation by isolating the exponential factor and taking logarithms
Problem
In this decay or half-life model, when does the target occur: \(A(t)=80(0.5)^{t/6}\) reaches \(10\)?
Big Picture
What this problem is really about
First express the target as a fraction of the initial amount. In a half-life model, rewrite that fraction as a power of one half; matching bases then tells how many half-life intervals have passed. Finally convert that interval count into elapsed time using the scale built into the exponent.
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