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=(A(t+1)-A(t))/(A(t)) \\ d=(A(t+1))/(A(t))-1 \\ d=(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%.