The wind speed is tracked as a storm approaches. The maximum speed w of wind gusts, in miles per hour, t hours after midnight on the night of an approaching storm is given in the figure.
a. Find the slope of the secant line that passes through points (1, 17.2) and (3, 26.9). Interpret your answer as an average rate of change over the interval 1 ≤ t ≤ 3.
b. Repeat the procedure outlined in part (a) for the secant line that passes through points (7, 34.4) and
c. Notice that the curve in the figure is generally increasing until t = 6, and is generally decreasing after
Give a plausible explanation for this behavior.
◦ a. 4.85, the wind is increasing in speed at an average rate of 4.85 mph per hour
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph per hour
c. The storm reached its closest point about 6:00 a.m. and is moving away after that.
◦ a. 9.7, the wind is increasing in speed at an average rate of 9.7 mph per hour
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph per hour
c. The storm reached its closest point about 6:00 a.m. and is moving away after that.
◦ a. 4.85, the wind is increasing in speed at an average rate of 4.85 mph
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph
c. The storm reached its farthest point about 6:00 a.m. and is moving closer after that.
◦ a. 4.85, the wind is increasing in speed at an average rate of 4.85 mph
b. -3.4, the wind speed is decreasing in speed at an average rate of 3.4 mph
c. The storm reached its closest point about 6:00 a.m. and is moving away after that.
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