Answer:
Option A - 4 years
Step-by-step explanation:
Given : Mike and Beatrice purchase a house for $200,000. If the equation [tex]V = 200000(1.03)^x[/tex] represents the value of the house after x years.
To find : How many years will it take the house to be worth approximately $225,000?
Solution :
The given equation is [tex]V = 200000(1.03)^x[/tex]
x is the number of years and V is the price of house.
In how many years the price became $225,000
V=$225,000
Substitute in the equation,
[tex]V = 200000(1.03)^x[/tex]
[tex]225000 = 200000(1.03)^x[/tex]
[tex]\frac{225000}{200000}=(1.03)^x[/tex]
[tex]1.125=(1.03)^x[/tex]
Taking log both side,
[tex]\log(1.125)=\log((1.03)^x)[/tex]
Apply logarithmic formula, [tex]\log(a)^x=x\log(a)[/tex]
[tex]\log(1.125)=x\log(1.03)[/tex]
[tex]\frac{\log(1.125)}{\log(1.03)}=x[/tex]
[tex]3.98=x[/tex]
Approximately x=4 years.
Therefore, Option A is correct.
