solve (15(0.95)^(n+1))=20(0.94)^(n),n

Question

mathstudent55 · Answer

Is this the equation?

$\large 15(0.95)^{n + 1} = 20 (0.94^n) $

anonymous · Answer

Yes

mathstudent55 · Answer

First, divide both sides by 20.

anonymous · Answer

It okay, I solved it

mathstudent55 · Answer

$\large 0.75(0.95)^{n + 1} = 0.94^n$

$\large 0.75(0.95^n)(0.95) = 0.94^n$

$\large (0.95)(0.75)(0.95^n) = 0.94^n$

$ \large( \dfrac{0.95}{0.94} \large)^n = 0.95^{-1}0.75^{-1} $

$\large \ln (\dfrac{0.95}{0.94}\large)^n = \ln (0.95^{-1}0.75^{-1} $)

$n\ln \dfrac{0.95}{0.94} = -\ln 0.95 - \ln 0.75 $

$n(  \ln 0.95 - \ln 0.94) = -\ln 0.95 - \ln 0.75 $

$n   = \dfrac{-\ln 0.95 - \ln 0.75}{   \ln 0.95 - \ln 0.94        } $

mathstudent55 · Answer

$n   = -\dfrac{\ln 0.95 + \ln 0.75}{   \ln 0.95 - \ln 0.94 }$

$n \approx 32.033$