91Ó°ÊÓ

The theoretical relationship between the variables is distance$=490{\left(time\right)}^2$

a. A graph of distance vs time square would roughly follow a straight line; this is because distance$=490{\left(time\right)}^2$, and so $y=490x$would be the straight line.

b. A graph of $\sqrt{dis\tan ce}$vs time would roughly follow a straight line, because taking the square root of either side of distance$=490{\left(time\right)}^2$results in $\sqrt{dis\tan ce}=\sqrt{490}$time, and so $y=\sqrt{490}x$would be the straight line.

c. A graph of distance versus $\sqrt{time}$would not roughly follow a straight line; this is because the distance$=490{\left(time\right)}^2$, and therefore there is a linear connection between distance and ${\left(time\right)}^2$, but not between distance and $\sqrt{time}$.

d. The pattern in a dotted figure of a power model can be straightened by taking the logarithm of each side. This is because the distance$=490{\left(time\right)}^2$is a power model (as taking the power of time) and it can straighten the pattern in a dotted figure of a power model by taking the logarithm of each side.

e. A graph of log distance versus log time would resemble a straight line. This is because the distance$=490{\left(time\right)}^2$is a power model (as we take the power of time) and it can straighten the pattern in a dotted figure of a power model by taking the logarithm of each side.

The correct option is (c).