To determine the rate of change in a situation where contestants are voted off a reality TV show each week, we need to analyze the graph that shows the number of contestants remaining over time (or episodes). The rate of change can be defined as how much the quantity (number of contestants) decreases with each vote-off episode.
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Identify Points on the Graph: First, observe the graph's coordinates (number of contestants at the start of the season and the number remaining after each episode).
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Calculate Changes: Look at the number of contestants before and after each voting episode. For example, if you notice that there were 10 contestants initially, and after the first week there are 8 contestants left, the change here is -2 contestants (10 - 8 = 2).
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Compute the Rate of Change: The rate of change is calculated as: \[ \text{Rate of Change} = \frac{\text{Change in Number of Contestants}}{\text{Change in Time (Weeks or Episodes)}} \] In the above example, if this decrease happened over 1 week (1 episode), the rate of change would be: \[ \text{Rate of Change} = \frac{-2}{1} = -2 \text{ contestants/week} \]
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Repeat for Each Episode: Do this calculation for each voting event to see if the rate of change remains constant or varies (e.g., if they voted off different numbers of contestants in subsequent weeks).
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Final Result: The rate of change will give you an understanding of how aggressively the contestants are being eliminated over the course of the show.
Without specific numerical values from the graph, we can conclude that the rate of change is found using the formula above and depends on the specific data points shown in the graph. If you have exact numbers, apply them to calculate the precise rate of change.