If the value of land in an area is increasing 6 percent a year, how long will it take for property values to double?

It will take 11.9 years for the property value to double.

Step-by-step explanation:

The value of the land is modeled by the following equation:

In which P(t) is the value after t years, P(0) is the initial value and r is the growth rate, as a decimal.

In this problem, we have that:

How long will it take for property values to double?

This is t when . So

We have that:

So to find t, we apply log to both sides of the equality.

It will take 11.9 years for the property value to double.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: