Austin bought a new house. The value of his house is modeled by the function H\left( x \right) = 120000{\left( {1.20} \right)^{\left( {\frac{1}{2}x} \right)}} where x is the number of years since he purchased the house. Looking at the model by what approximate percentage rate is the value of his house increasing? HHHHHHHEEEEEEELLLLLLPPPPP!!!!!!!!!

Question

Austin bought a new house.  The value of his house is modeled by the function H\left( x \right) = 120000{\left( {1.20} \right)^{\left( {\frac{1}{2}x} \right)}} where x is the number of years since he purchased the house.  Looking at the model by what approximate percentage rate is the value of his house increasing? HHHHHHHEEEEEEELLLLLLPPPPP!!!!!!!!!

Steve · Answer

Sorry - not much TeX here. It appears that you mean

H(x) = 120000*1.20^(1/2 x)
That means that H grows by 20% every 2 years. But, if we want an annual rate, then we have to realize that this is the same as

H(x) = 120000*(√1.2)^x
√1.2 = 1.095
So, we wind up with

H(x) = 120000*1.095^x

So, the annual appreciation is about 9.5%