A home's value increases at an average rate of \( 5.5 \% \) each year. The current value is \( \$ 120,000 \). What function can be used to find the value of the home after \( x \) years? \( f(x)=120,000(1.055 x) \) \( f(x)=120,000(0.055)^{x} \) \( f(x)=120,000(1.055)^{x} \) \( f(x)=[(120,000)(1.055)]^{x} \)
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To model the increase in a home's value over time, you would use an exponential growth function. The correct choice for the value of the home after \( x \) years is \( f(x) = 120,000(1.055)^{x} \). This equation represents the current value multiplied by the growth factor \( 1.055 \) raised to the power of \( x \), which is the number of years. It's worth noting that the other options provided don't represent the correct exponential growth model. For instance, the option \( f(x)=120,000(0.055)^{x} \) incorrectly applies the percentage, making it decrease instead of grow, while \( f(x)=[(120,000)(1.055)]^{x} \) implies a compounding of both the initial value and growth, which isn’t how exponential growth works in this scenario. Always remember the proper use of the base in growth functions for accurate modeling!
