Question

A population triples every 6 months. How long, in months, does it take to double?

a. 3
b. 4
c.
`(6ln2)/(ln3)`
d. 6 ln 2-ln 3
e. 6(ln 2 - ln 3)

Answer 1

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:


`{ 3 }^{ \frac { m }{ 6 } }\cdot P`

M=Months

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Now:


`{ 3 }^{ \frac { m }{ 6 } }P=2P\\ \\ { 3 }^{ \frac { m }{ 6 } }=2\\ \\ \log _( 3 ){ 2 } =\frac { m }{ 6 }`


`\\ \\ m=6\cdot \log _( 3 ){ 2 } \\ \\ =6\cdot \frac { \ln { 2 } }{ \ln { 3 } } \\ \\ =\frac { 6\ln { 2 } }{ \ln { 3 } }`