From the question we can determine the following information;
WHAT YOU KNOW:
Initial value of the house is 160,000
The rate of increase per year is 7%
The time over which the value has been increasing in value is 20 years
WHAT THE QUESTION IS ASKING:
The increment is a fixed percentage on the current value for every given year, which means its value increases at an exponential rate. This means we want to determine the function which would be used to find the value at any particular year from inception till the current year. After that we would calculate the value of the house today, that is 20 years after it was bought.
WORKINGS:
The general formula for an exponential growth is given as;
[tex]f(x)=a(1+r)^x[/tex]Where the variables are;
[tex]\begin{gathered} a=\text{initial value,} \\ r=\text{rate of growth (given as a decimal)} \\ x=\text{time period (in years)} \end{gathered}[/tex]The value after 20 years would now be;
[tex]\begin{gathered} f(x)=a(1+r)^x \\ \text{For a 20 year period, we would substitute for x=20} \\ f(20)=160000(1+0.07)^{20} \\ f(20)=160000(1.07)^{20} \\ f(20)=160000(3.86968) \\ f(20)=619148.8 \end{gathered}[/tex]This means the house that was bought for $160,000 20 years ago and whose value incresed by 7% per year is now worth $619,148.80.