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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

Sagot :

Given equation,

[tex]y=350e^{-0.07t}[/tex]

The continuous decay rate is the differential of the function

Thus,

[tex]\begin{gathered} \frac{dy}{dt}=\frac{d}{dt}(350e^{-0.07t}) \\ =350(-0.07)e^{-0.07t} \end{gathered}[/tex]

Thus the rate of continuous deacay is:

[tex]\begin{gathered} \frac{\frac{dy}{dt}}{y}\times100\%=\frac{350(-0.07)e^{-0.07t}}{350e^{-0.07t}}\times100\% \\ =-0.07\times100\% \\ =-7\% \end{gathered}[/tex]

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

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