\(y=Ae^{kt}+c\qquad A>0,\ k\ne0\)
Growth: \(k>0\). Decay towards \(c\): \(k<0\). More generally, the sign of \(Ak\) determines whether the model increases or decreases.
| Part of the model | Meaning |
|---|---|
| \(t=0\) | |
| \(k>0\) | |
| \(k<0\) | |
| \(y=c\) |
\(k>0\): growth away from the initial value.
\(k<0\): decay towards the limiting value \(y=c\) (dashed).
Finding time
\(t=\dfrac1k\ln\!\left(\dfrac{y-c}{A}\right)\qquad\dfrac{y-c}{A}>0\)
Use the initial value to find \(A\), then another data point to find \(k\). State units and round only the final answer.
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