Answer:
The rate of change of house value after 11 years is 4.89
Step-by-step explanation:
Given as ;
The principal cost of house = $ 144,000
The time period = 11 years
The amount of house after 11 years = $245,000
Let The rate of change = R
Now,
The cost of house after n years = Initial cost of house × [tex](1+\dfrac{\textrm Rate}{\textrm Time})^{n}[/tex]
Or, $245,000 = $ 144,000 × [tex](1+\dfrac{\textrm R}{\textrm 100})^{11}[/tex]
Or, [tex]\frac{245,000}{144,000}[/tex] = [tex](1+\dfrac{\textrm R}{\textrm 100})^{11}[/tex]
Or, 1.7013 = [tex](1+\dfrac{\textrm R}{\textrm 100})^{11}[/tex]
Or, [tex](1.7013)^{\frac{1}{11}}[/tex] = ( 1 + [tex]\dfrac{\textrm R}{100}[/tex] )
Or , 1.04898 = ( 1 + [tex]\dfrac{\textrm R}{100}[/tex] )
Or, 1.04898 - 1 = [tex]\dfrac{\textrm R}{100}[/tex]
So, 0.04898 = [tex]\dfrac{\textrm R}{100}[/tex]
Or, 0.04898 × 100 = R
∴ R = 4.89
Hence The rate of change of house value after 11 years is 4.89 Answer
