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Question 1 (1 point) What is the rate of growth or rate of decay? \[ y=5575(0.65)^{x} \] a \( x \) b 5575 c \( \quad .65 \) d 1

Ask by Vargas Weston. in the United States
Feb 26,2025

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The rate of decay is 0.65.

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The equation you provided, \( y = 5575(0.65)^{x} \), exhibits decay rather than growth because the base is less than 1. Specifically, the 0.65 means that for each unit increase in \( x \), the value of \( y \) is multiplied by 0.65, indicating a reduction over time. This is a common feature in exponential decay models, such as those used to track radioactive decay or depreciation of assets. In this context, the rate of decay can be extracted from the base of the exponential. The specific decay rate of 0.65 indicates a 35% decrease (which is 1 - 0.65) in the value for every increase of 1 in \( x \). This rate is pivotal when modeling systems that lose value over time, such as a car depreciating on the lot!

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