Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.3 - Analyzing Graphs of Functions - 2.3 Exercises - Page 196: 68


a) $s=-16t^2+72t+6.5$ b) See graph c) $8$ d) Positive slope e) $y=8t+6.5$ f) See graph

Work Step by Step

a) The function representing the position is: $s=-16t^2+v_0t+s_0$ where $v_0$ is the velocity and $s_0$ is the height from which the object is thrown. We are given: $s_0=6.5$ $v_0=72$ The equation of the position is: $s=-16t^2+72t+6.5$ b) Graph the function. c) Determine the average rate of change from $t_1=0$ to $t_2=4$: $\dfrac{s(t_2)-s(t_1)}{t_2-t_1}=\dfrac{s(4)-s(0)}{4-0}$ $=\dfrac{[-16(4^2)+72(4)+6.5]-[-16(0^2)+72(0)+6.5]}{3}$ $=\dfrac{32}{4}$ $=8$ d) Notice that the slope of the secant line is positive. e) Determine the equation of the secant using the slope $m=4$ and the point $(0,s(0))=(0,-16(0^2)+72(0)+6.6)=(0,6.5) $: $y-6.5=8(t-0)$ $y=8t+6.5$ f) Graph the secant line:
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