- The home value decreases by 7.1% each year. - This means the home retains 92.9% (100% - 7.1%) of its value each year. - The equation for the value of the home after \(t\) years is given by multiplying the original value by \(0.929\) raised to the power of \(t\).

 - Therefore, the correct model is \(V( t) = 249,000( 0.929) ^ t\). 

Supplemental Knowledge

Exponential decay is a process where a quantity decreases at a consistent percentage rate over time. The general formula for modeling exponential decay is: \[V( t) = V_ 0 \cdot ( 1 - r) ^ t\] where: - \(V( t) \) is the value after \(t\) years, - \(V_ 0\) is the initial value, - \(r\) is the decay rate (expressed as a decimal), - \(t\) is the number of years. In this scenario, the initial value of the home (\(V_ 0\)) is 249,000, and it decreases by 7.1% each year. To express 7.1% as a decimal, we convert it to 0.071. 

Applied Knowledge

Think about all of the items that depreciate over time - cars, electronics and even houses in certain markets. An exponential decay model allows us to predict a depreciating car over time using its purchase cost as an example; homeowners track property values to understand market fluctuations affecting investments like houses; being informed on depreciation models helps make informed decisions when selling or refinancing a home.

Understanding exponential decay can be crucial for financial planning and investment strategies! For more practice with exponential functions or other math topics, explore UpStudy’s live tutor question bank or AI-powered problem-solving services! Visit UpStudy today and elevate your learning experience with personalized support tailored just for you!