0 Months = P
6 Months = (3^1)P
12 Months = (3^2)P
18 Months = (3^3)P
24 Months = (3^4)P
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Equation for the function:
[tex]{ 3 }^{ \frac { m }{ 6 } }\cdot P[/tex]
M=Months
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Now:
[tex]{ 3 }^{ \frac { m }{ 6 } }P=2P\\ \\ { 3 }^{ \frac { m }{ 6 } }=2\\ \\ \log _{ 3 }{ 2 } =\frac { m }{ 6 }[/tex]
[tex]\\ \\ m=6\cdot \log _{ 3 }{ 2 } \\ \\ =6\cdot \frac { \ln { 2 } }{ \ln { 3 } } \\ \\ =\frac { 6\ln { 2 } }{ \ln { 3 } } [/tex]
