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Write a function in terms of \( t \) that represents the situation. A smartphone costs \( \$ 850 \), and its resell value decreases by \( 11.2 \% \) each year. \( y=850 \times 0.888^{t} \) Basic

Ask by Harris Gibbs. in the United States
Jan 24,2025

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The resale value of the smartphone after \( t \) years is given by \( y = 850 \times 0.888^{t} \).

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The function you've written captures the essence of how the smartphone's value declines over time due to depreciation. Each year, the smartphone retains \( 88.8\% \) of its value, represented by the factor \( 0.888 \). To visualize your investment, consider that after 1 year, the value drops to approximately \( \$ 754.80 \), and by the end of the second year, you can expect it to be around \( \$ 670.66 \). If we plug in more values for \( t \), we can see the trend more clearly. For example, at \( t = 3 \), the value shrinks to about \( \$ 594.62 \). This exponential decay function gives you a powerful tool to forecast the resale value of the smartphone effectively throughout its useful lifetime, helping you make smarter buying and selling decisions.

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