Respuesta :
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:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
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:
[tex]r = 0.06[/tex]
How long will it take for property values to double?
This is t when [tex]P(t) = 2P(0)[/tex]. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]2P(0) = P(0)(1+0.06)^{t}[/tex]
[tex](1.06)^{t} = 2[/tex]
We have that:
[tex]\log{a^{t}} = t\log{a}[/tex]
So to find t, we apply log to both sides of the equality.
[tex]\log{(1.06)^{t}} = \log{2}[/tex]
[tex]t\log{1.06} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.06}}[/tex]
[tex]t = 11.9[/tex]
It will take 11.9 years for the property value to double.
