Find a Power Function That Models the Data in the Table

question 132

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The height of a projectile moving vertically is given by the table, where t is the elapsed time in seconds and h is the height in feet. $\begin{array}{r|rrrrrr}\mathrm{t} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{h} & 100 & 684 & 1236 & 1756 & 2244 & 2700\end{array}$

If the height is modeled by $h ( t ) = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 }$ , where $v _ { 0 }$ and $h _ { 0 }$ are the velocity and height at $t = 0$ , respectively, find $\mathrm { v } _ { 0 }$ .

• A) \(700 \mathrm { ft } / \mathrm { sec }\)
• B) \(600 \mathrm { ft } / \mathrm { sec }\)
• C) \(1200 \mathrm { ft } / \mathrm { sec }\)
• D) \(350 \mathrm { ft } / \mathrm { sec }\)

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