$\"\"$

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

\

The amount is doubled in $\"\"$

\

The amount $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

Apply natural logarithm on each side.

\

$\"\"$

\

Power rule of logarithms: $\"\"$ .

\

$\"\"$

\

since $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

\

The period of time $\"\"$ .

\

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

\

The total amount is

\

$\"\"$

\

The total amount after 10 years is $\"\"$ .

\

$\"\"$

\

The completed table is:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Initial investment	Annual rate	Time to double	Amount after 10 years
$\"\"$	\ $\"\"$ \	$\"\"$	$\"\"$