Question

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

Answer 1

Answer:

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:

$P(t) = P(0)(1+r)^{t}$

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:

$r = 0.06$

How long will it take for property values to double?

This is t when $P(t) = 2P(0)$. So

$P(t) = P(0)(1+r)^{t}$

$2P(0) = P(0)(1+0.06)^{t}$

$(1.06)^{t} = 2$

We have that:

$\log{a^{t}} = t\log{a}$

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

$\log{(1.06)^{t}} = \log{2}$

$t\log{1.06} = \log{2}$

$t = \frac{\log{2}}{\log{1.06}}$

$t = 11.9$

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