Math  /  Data & Statistics

Question\begin{tabular}{|c||c|c|c|c|c|c|c|} \hline \begin{tabular}{c} tt \\ (in seconds) \end{tabular} & 0.1 & 0.5 & 0.9 & 1.5 & 1.9 & 2.3 & 2.6 \\ \hline \begin{tabular}{c} H(t)H(t) \\ (in meters) \end{tabular} & 1.4 & 5.7 & 8.4 & 9.6 & 8.4 & 5.6 & 2.5 \\ \hline \end{tabular}
1. Justin Tucker, the kicker for the Baltimore Ravens, is considered one of the greatest kickers in NFL history. On a recent kickoff, the height of the ball, in meters, was measured for selected times. This data is shown in the table above. a) Based on this situation and the data presented in the table, would a linear, quadratic, or cubic function be most appropriate to model this data? Give a reason for your answer. b) Find the appropriate regression function to model these data. c) Using the model found in part bb, what is the predicted height of the football, in meters, at tine t=1.3t=1.3 seconds?

Studdy Solution
Use the quadratic model to predict the height at t=1.3 t = 1.3 seconds:
Substitute t=1.3 t = 1.3 into the regression equation: H(1.3)=2.5(1.3)2+10(1.3)+0.5 H(1.3) = -2.5(1.3)^2 + 10(1.3) + 0.5
Calculate: H(1.3)=2.5(1.69)+13+0.5 H(1.3) = -2.5(1.69) + 13 + 0.5 H(1.3)=4.225+13+0.5 H(1.3) = -4.225 + 13 + 0.5 H(1.3)=9.275 H(1.3) = 9.275
The predicted height at t=1.3 t = 1.3 seconds is approximately 9.275 9.275 meters.
The predicted height is:
9.275 meters \boxed{9.275 \text{ meters}}

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