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# Average Rate Of Change And Equations

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### Average Rate Of Change And Equations

1. 1. Average Rate of Change and Equations…
2. 2. Do Now: The height, in feet, of a ball thrown into the air is modeled by h(t) = - 16t 2 – 96t , where t is measured in seconds. Graph the height of the ball seconds on the following grid. Use a scale on the x -axis of 3 boxes = 1 second. On the y­ -axis use 5 boxes = 40 feet. <ul><li>How far did the ball travel from t = 0 to t = 2 seconds? </li></ul><ul><li>128 Ft </li></ul><ul><li>What was the average distance traveled for the first two seconds? </li></ul><ul><li>64 ft per second </li></ul><ul><li>What is another name for this? </li></ul><ul><li>average velocity </li></ul><ul><li>Draw a line connecting (0, h (0)) and (2, h (2)). What is this line? </li></ul><ul><li>secant line </li></ul><ul><li>What does the average distance traveled (per second) represent in terms of this line? </li></ul><ul><li>slope </li></ul><ul><li>Write the equation of this line. </li></ul><ul><li>y – 0 = 64(x – 0) or y – 128 = 64(x – 2) </li></ul>
3. 3. In general, __________________________________, can be found by using the formula: The average rate of change of a function (slope of the secant) Where [a,b] is a closed interval on which f is defined
4. 4. The equation of ___________________________, can be found by: <ul><li>1. Finding the slope of the secant (AROC) </li></ul><ul><li>2. using point/slope with either point </li></ul>The secant line
5. 5. <ul><li>In general, as the interval get smaller (as b gets closer to a ), what line are we approximating? </li></ul><ul><li>tangent line </li></ul><ul><li>In terms of the original problem, what does this represent? </li></ul><ul><li>Instantaneous velocity </li></ul><ul><li>In general, how can we represent this? </li></ul>