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
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
Solution
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 \( 0.36 \).