To determine the equation that represents the value of Hadlee's home [tex]\( x \)[/tex] years after purchase, we need to understand the concept of exponential growth.
1. Initial Value and Growth Rate:
- The initial value of Hadlee's home is \$220,000.
- The annual growth rate is 4%, which can be written as 0.04 in decimal form.
2. Growth Formula:
The general formula for exponential growth is [tex]\( P(t) = P_0 (1 + r)^t \)[/tex], where:
- [tex]\( P(t) \)[/tex] is the value after [tex]\( t \)[/tex] years,
- [tex]\( P_0 \)[/tex] is the initial value,
- [tex]\( r \)[/tex] is the growth rate,
- [tex]\( t \)[/tex] is the time in years.
3. Applying Values:
- Here, [tex]\( P_0 = 220,000 \)[/tex],
- [tex]\( r = 0.04 \)[/tex],
- [tex]\( t = x \)[/tex].
Therefore, the equation becomes:
[tex]\[
P(x) = 220000(1 + 0.04)^x = 220000(1.04)^x
\][/tex]
Thus, the correct equation that can be used to represent the value of the home [tex]\( x \)[/tex] years after purchase is:
[tex]\[
f(x) = 220000(1.04)^x
\][/tex]
Out of the given options, the correct answer is:
[tex]\[
f(x)=220000(1.04)^x
\][/tex]
