The value of a $225,000 house increases at a rate of 3.5% each year. use a graph to predict the value of the house in 8 years.
a) ≈ $276,582
b) ≈ $286,263
c) ≈ $306,652
d) ≈ $296,282

In order to determine the value of the rent after x years, we need to generate a function which would relate the value of the rent and the time in years. The rate by which the rent increases is said to be 3.5% per year. So, if we do it manually, we would have:

value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) +

However, this is a tedious and long process since we need to continue until year 8. We need to simplify it to an expression. We do as follows:

value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) +

We factor out the initial rent, 

value of the rent = 225000 (1 + (.035) + (.035)(.035) + )

Then, we simplify the terms inside the first parentheses,

value of the rent = 225000 (1 + (.035))^x

where x is the number of years. We then substitute 8 to x to determine the value of the rent.

value of the rent = 225000 (1 + (.035))^8 = 296282.03