Answer:
The number of years in which house value goes up is 145 years .
Step-by-step explanation:
Given as :
The initial purchased value of the house = p = $179,300,00
The value of house goes up every years at the rate = r = 4%
Let The number of years in which house value goes up = t years
The value of the house after t years = $A = $5197,230,002
Now, According to question
The value of the house after t years = The initial purchased value of the house × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
I.e A = $p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or,$5197,230,002 = $17930000 × [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]
Or, [tex]\dfrac{5197,230,002}{179,300,00}[/tex] = [tex](1+\dfrac{\textrm 4}{100})^{\textrm t}[/tex]
Or, 289.86 = [tex](1.04)^{t}[/tex]
Now, taking Log both side
So, [tex]Log_{10}[/tex]289.86 = [tex]Log_{10}[/tex] [tex](1.04)^{t}[/tex]
or, 2.462 = t × [tex]Log_{10}1.04
or, 2.462 = t × 0.01703
∴ t = [tex]\dfrac{2.462}{0.01703}[/tex]
I.e t = 144.56 ≈ 145
So, Number of years = t = 145 years
Hence The number of years in which house value goes up is 145 years . Answer
