Questions: Estimate the average rate of change from when x=3.1 to when x=5.89. (1 point) approximately 6 approximately 0.5 approximately 0.17 approximately -0.17

Estimate the average rate of change from when x=3.1 to when x=5.89. (1 point) approximately 6 approximately 0.5 approximately 0.17 approximately -0.17
Transcript text: Estimate the average rate of change from when $x=3.1$ to when $x=5.89$. (1 point) approximately 6 approximately 0.5 approximately 0.17 approximately -0.17
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Solution

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Solution Steps

Step 1: Identify the coordinates at the given x-values
  • At \( x = 3.1 \), the y-coordinate is approximately 4.
  • At \( x = 5.89 \), the y-coordinate is approximately 5.
Step 2: Calculate the change in y-values
  • Change in y-values: \( 5 - 4 = 1 \).
Step 3: Calculate the change in x-values
  • Change in x-values: \( 5.89 - 3.1 = 2.79 \).
Step 4: Calculate the average rate of change
  • Average rate of change: \( \frac{\text{Change in y-values}}{\text{Change in x-values}} = \frac{1}{2.79} \approx 0.36 \).

Final Answer

  • The average rate of change is approximately \( 0.36 \).
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