Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve an exponential equation of the form ab^(ct)=d by isolating the exponential factor and taking logarithms
Problem
For the growth model \(P(t)=1000(1.04)^t\), when does \(P(t)\) reach \(2000\)?
Big Picture
What this problem is really about
Turn the target amount into a target growth factor by dividing out the initial amount first. Logarithms then bring the unknown time down from the exponent, producing a quotient of logarithms. Preserve that exact quotient until the final evaluation, and attach the model's time unit to the interpretation.
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