Respuesta :
Answer:
The annual growth rate is of 1.39%.
The value of the house in 2010 was $155,355.5
Step-by-step explanation:
The value of a house after t years is given by the following equation:
[tex]V(t) = V_{0}(1 + r)^{t}[/tex]
In which [tex]V_{0}[/tex] is the initial value and r is the annual growth rate.
In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $145,000. What was the annual growth rate between 1985 and 2005?
We want to find r, when [tex]V_{0} = 110[/tex] and [tex]V(20) = 145[/tex].
I use V(20) since 2005 is 20 years after 1985.
So
[tex]V(t) = V_{0}(1 + r)^{t}[/tex]
[tex]145 = 110(1 + r)^{20}[/tex]
[tex](1 + r)^{20} = 1.3182[/tex]
Applying the 20th root to both sides.
[tex]1 + r = 1.0139[/tex]
[tex]r = 0.0139[/tex]
So the annual growth rate is of 1.39%.
What was the value of the house in the year 2010?
2010 is 25 years after 1985. So
[tex]V(t) = 110(1.0139)^{t}[/tex]
[tex]V(25) = 110(1.0139)^{25} = 155.3355[/tex]
The value of the house in 2010 was $155,355.5
