Asked by Jenn
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!!!!!!!!!
Answers
Answered by
Steve
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%
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%
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