Chapter 12.2, Problem 52E

To determine

To find: the following scatter figure that would not follow a straight line.

Answer to Problem 52E

A figure of distance versus $\sqrt{\text{time}}$

Explanation of Solution

Given:

  $\text{distance =490}{\left(\text{time}\right)}^2$

1. A figure of distance versus ${\text{time}}^2$ would be approximately following a straight line, the reason is $\text{distance =490}{\left(\text{time}\right)}^2$ and therefore $y=490x$ would be the straight line.
2. A figure of $\sqrt{\text{distance}}$ versus time would be approximately follow a straight line, the reason is that the taking the square root of each side of $\text{distance=490}{\left(\text{time}\right)}^2$ result in $\sqrt{\text{distance}}\text{ =}\sqrt{\text{490}}\text{time}$ and therefore $y=\sqrt{490x}$ would be the straight line.
3. A figure of distance versus $\sqrt{\text{time}}$ would not be approximately follow a straight line, the reason is that the $\text{distance}=490{\left(\text{time}\right)}^2$ and therefore there is a linear relationship between distance and ${\left(\text{time}\right)}^2$ but not between distance and $\sqrt{\text{time}}$ .
4. A figure of in distance versus in time would be approximately follow a straight line, the reason is that $\text{distance}=490{\left(\text{time}\right)}^2$ is a power model (as taking the power of time) and it can straight the pattern in a dot figure of a power model by taking the logarithm of each side.
5. A figure of log distance versus log time would be approximately follow a straight line, the reason is that the $\text{distance}=490{\left(\text{time}\right)}^2$ is a power model (as we take the power of time) and it can straight the pattern in a dot figure of a power model by taking the logarithm of each side.

Hence, the correct option is (c)