Question

Write the exponential function y = 350e^-0.07t in the form y - Pa^thelp solve C (a) Once you have rewritten the formula, give a accurate to at least four decimal places.a =e^(-0.07)(b) The annual decay rate is 6.76(c) The continuous decay rate is ___% per year

Answer 1

Given equation,

`y=350e^(-0.07t)`

The continuous decay rate is the differential of the function

Thus,

`\begin{gathered} (dy)/(dt)=(d)/(dt)(350e^(-0.07t)) \\ =350(-0.07)e^(-0.07t) \end{gathered}`

Thus the rate of continuous deacay is:

`\begin{gathered} ((dy)/(dt))/(y)*100\%=(350(-0.07)e^(-0.07t))/(350e^(-0.07t))*100\% \\ =-0.07*100\% \\ =-7\% \end{gathered}`

Thus the cotinuous decay rate per year is -7%.