$\"\"$

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

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The amount is doubled in $\"\"$ years.

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The amount $\"\"$ .

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Compounded continuously.

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Formula for continuous compounding : $\"\"$ .

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$\"\"$

\

$\"\"$

\

Take ln on each side.

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$\"\"$

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Apply power rule of logarithms : $\"\"$ .

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$\"\"$

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Substitute the value of $\"\"$ .

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$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in the above equation.

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$\"\"$

\

The amount double in $\"\"$ .

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$\"\"$

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

\

The period of time $\"\"$ .

\

Formula for continuous compounding : $\"\"$ .

\

The total amount is

\

$\"\"$

\

The total amount after $\"\"$ is $\"\"$ .

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$\"\"$

\

The amount double in $\"\"$ .

\

The total amount after $\"\"$ is $\"\"$ .