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Help would be much appreciated

Help would be much appreciated-example-1
User Obed
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1 Answer

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Answer:


r(t)=(1)/(t)\ln \left((A)/(P)\right)

Explanation:

Given function:


A(t)=Pe^(rt)

Divide both sides by P:


\implies (A)/(P)=e^(rt)

Take natural logs of both sides of the equation:


\implies \ln \left((A)/(P)\right)=\ln e^(rt)


\textsf{Apply the power law}: \quad \ln x^n=n \ln x


\implies \ln \left((A)/(P)\right)=rt\ln e

Apply the natural log law: ln (e) = 1


\implies \ln \left((A)/(P)\right)=rt

Divide both sides by t:


\implies r=(1)/(t)\ln \left((A)/(P)\right)

User Jedie
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