Find a Power Function That Models the Data in the Table

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) $350 \mathrm { ft } / \mathrm { sec }$