Question

What’s the decay percentage of A=400e^-0.079t

Answer 1

We have an exponential decay model expressed as:

$A(t)=400\cdot e^{-0.079t}$

We can express the the decay as the variation between consecutive terms, like A(t+1) and A(t), relative to a A(t).

We can express this as:

$\begin{gathered} d=\frac{A(t+1)-A(t)}{A(t)} \\ d=\frac{A(t+1)}{A(t)}-1 \\ d=\frac{400e^{-0.079(t+1)}}{400e^{-0.079t}}-1 \\ d=e^{-0.079}-1 \\ d\approx0.92404-1 \\ d\approx-0.07596\approx-7.60\% \end{gathered}$

We then can conclude that the decay for this model is 7.60%.

NOTE: the decay d is negative as A decreases with the increase in t.

Answer: the decay percentage is 7.60%.