To compare the estimated average rate of change of the quadratic function on the interval [0, 5] to the estimated average rate of change of the exponential function \( y = -6x \) on the same interval, we first need to calculate the average rates of change for both functions.
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Quadratic Function: Let's denote the quadratic function as \( f(x) \). To find the average rate of change on the interval [0, 5], we use the formula: \[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \] where \( a = 0 \) and \( b = 5 \).
Assuming from the graph that \( f(0) \) and \( f(5) \) can be estimated (you would take the corresponding y-values for these x-values from the graph). Suppose, for instance, \( f(0) \approx 10 \) and \( f(5) \approx 50 \) (these need to be derived from the actual plotted points).
Then: \[ \text{Average Rate of Change} = \frac{f(5) - f(0)}{5 - 0} = \frac{50 - 10}{5} = \frac{40}{5} = 8. \]
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Exponential Function: Now, we'll calculate the average rate of change for \( y = -6x \) on the same interval: \[ y(0) = -6(0) = 0, \] \[ y(5) = -6(5) = -30. \] Using the same average rate of change formula: \[ \text{Average Rate of Change} = \frac{-30 - 0}{5 - 0} = \frac{-30}{5} = -6. \]
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Comparison: Now we can compare the average rates of change we calculated:
- Average rate of change for the quadratic function: \( 8 \)
- Average rate of change for the exponential function: \( -6 \)
Since \( 8 > -6 \), we conclude: The estimated average rate of change of the quadratic function > the estimated average rate of change of the exponential function.
Therefore, the final statement is: The estimated average rate of change of the quadratic function > the estimated average rate of change of the exponential function.