Question

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

Answer 1

Is this the equation?

\(\large 15(0.95)^{n + 1} = 20 (0.94^n) \)

Answer 2

Yes

Answer 3

First, divide both sides by 20.

Answer 4

It okay, I solved it

Answer 5

\(\large 0.75(0.95)^{n + 1} = 0.94^n\)

\(\large 0.75(0.95^n)(0.95) = 0.94^n\)

\(\large (0.95)(0.75)(0.95^n) = 0.94^n\)

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

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

\(n\ln \dfrac{0.95}{0.94} = -\ln 0.95 - \ln 0.75 \)

\(n( \ln 0.95 - \ln 0.94) = -\ln 0.95 - \ln 0.75 \)

\(n = \dfrac{-\ln 0.95 - \ln 0.75}{ \ln 0.95 - \ln 0.94 } \)

Answer 6

\(n = -\dfrac{\ln 0.95 + \ln 0.75}{ \ln 0.95 - \ln 0.94 }\)

\(n \approx 32.033\)