Exponential growth is generally applied to word problems such as

compound interest problems and

population growth problems. To grow exponentially means that the topic being studied is increasing in

proportion to what was previously there. For example, money deposited in the bank earns interest that is added to the money previously in the bank.

First, we will need to use the exponential growth formula for compounding interest:

In the formula,

*A* represents the amount of money that will be in the account when $1200 is doubled.

*P* represents principal - the amount of money currently being invested. The letter

*r* stands for

rate of interest, and

*t* stands time in years. In this formula

*e* represents the

irrational number 2.71828…..

Now, we need to substitute known values for the variables in the formula. The problem asks how long it will take $1200 to double. Therefore,

*A* is 2400 (the value of 1200 doubled) in this problem.

*P* is the money to be invested, so

*P* is 1200. The rate,

*r,* is which is

or 0.105 as a decimal. Time

*t* is what we are trying to find. So we have the following:

Finally we must solve the

equation for time

*t*. To do so, first divide both sides by 1200 to simplify the equation.

Now, we take the natural log of each

side of the equation. For a reminder on taking the log of both sides as well as the properties of logs, please examine the material in this

companion lesson.

Using the following property of logs,

, we have:

Since the

is equal to 1, we will substitute 1 for

to give us the following:

Use a calculator to find the value for the ln 2 and then divide each

side by 0.105 to obtain the final answer:

Therefore, we have determined that if $1200 is invested at

compounded continuously, it will take 6.6 years for the money to double.