Question

Isaac purchased a house for $179,300,00. Every year, Isaac makes improvements so that the value of the house goes up by 4%.

Answer 1

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 × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

I.e A = $p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or,$5197,230,002 = $17930000 × $(1+\dfrac{\textrm 4}{100})^{\textrm t}$

Or, $\dfrac{5197,230,002}{179,300,00}$ = $(1+\dfrac{\textrm 4}{100})^{\textrm t}$

Or, 289.86 = $(1.04)^{t}$

Now, taking Log both side

So, $Log_{10}$289.86 = $Log_{10}$ $(1.04)^{t}$

or, 2.462 = t ×  $Log_{10}1.04or, 2.462 = t × 0.01703∴ t = [tex]\dfrac{2.462}{0.01703}$

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