`(1+0.09/12)^(12t) = 3` Solve the equation accurate to three decimal places

Tuesday, March 27, 2012

$\displaystyle{{\left({1}+\frac{{0.09}}{{12}}\right)}}^{{{12}{t}}}={3}$ Solve the equation accurate to three decimal places

$\displaystyle{{\left({1}+\frac{{0.09}}{{12}}\right)}}^{{{12}{t}}}={3}$

In solving these kind of problems we need to use the logarithm.

Take the log of both sides of the equation.

$\displaystyle{\log}_{{{10}}}{\left({{\left({1}+\frac{{0.09}}{{12}}\right)}}^{{{12}{t}}}\right)}={\log}_{{10}}{\left({3}\right)}$

With logarithms we know that;

$\displaystyle{\log{{\left({{a}}^{{b}}\right)}}}={b}{\log{{a}}}$

using that rule;

$\displaystyle{\log}_{{{10}}}{\left({{\left({1}+\frac{{0.09}}{{12}}\right)}}^{{{12}{t}}}\right)}={12}{t}{\log}_{{10}}{\left({1}+\frac{{0.09}}{{12}}\right)}$

$\displaystyle{12}{t}{\log}_{{10}}{\left({1}+\frac{{0.09}}{{12}}\right)}={\log}_{{10}}{\left({3}\right)}$

$\displaystyle{\log}_{{10}}{\left({1}+\frac{{0.09}}{{12}}\right)}={\log}_{{10}}{\left({1.0075}\right)}={0.003245}$

$\displaystyle{\log}_{{10}}{\left({3}\right)}={0.4771}$

$\displaystyle{12}{t}\times{0.003245}={0.4771}$

$\displaystyle{t}=\frac{{0.4771}}{{{12}\times{0.00325}}}={12.252}$

So the answer is t = 12.252

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Tuesday, March 27, 2012

$\displaystyle{{\left({1}+\frac{{0.09}}{{12}}\right)}}^{{{12}{t}}}={3}$ Solve the equation accurate to three decimal places

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Tuesday, March 27, 2012

Solve the equation accurate to three decimal places

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Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{{\left({1}+\frac{{0.09}}{{12}}\right)}}^{{{12}{t}}}={3}$ Solve the equation accurate to three decimal places

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?