Answer:
6 years.
Step-by-step explanation:
We have been given that a house that costs $270,000 appreciates by 5% each year. We are asked to find the number of years it will take the house to be worth 350,000 by using equation [tex]350=270*(1.05)^x[/tex].
First of all let us divide both sides of our equation by 270.
[tex]\frac{350}{270}=\frac{270*(1.05)^x}{270}[/tex]
[tex]\frac{350}{270}=(1.05)^x[/tex]
Upon taking natural log of both sides of our equation we will get,
[tex]ln(\frac{35}{27})=ln((1.05)^x)[/tex]
Using natural log property [tex]ln(a^b)=b*ln(a)[/tex] we will get,
[tex]ln(\frac{35}{27})=x*ln(1.05)[/tex]
[tex]0.2595111954850846=x*0.048790164169432[/tex]
[tex]x=\frac{0.2595111954850846}{0.048790164169432}[/tex]
[tex]x=5.31892441648[/tex]
Since it will take more time than 5 years, so will round up our answer.
[tex]x\approx 6[/tex]
Therefore, in approximately 6 years the house will be worth $350,000.
