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Chapter 7: Problem 17

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -3 \\ \hline 1 & 2 \\ \hline 2 & 7 \\ \hline 3 & 12 \\ \hline 4 & 17 \\ \hline \end{array} $$

Short Answer

Expert verified
The data is best modeled by a linear function.

Step by step solution

01

Create a scatter plot

Start by plotting each data point \( (x, y) \) given in the table on a graph. Plot the x-values along the horizontal axis, and the y-values along the vertical axis. Each point on the plot corresponds to a pair \( (x, y) \) from the table.
02

Observe the shape of the data

After plotting all the data points, observe the distribution of the data points. If the points lie along a straight line, it indicates a linear relationship. If the points form a curve that rises or falls sharply at first and then more slowly, it indicates an exponential or logarithmic function. And if the data points form a kind of 'U' or 'n' shape, it indicates a quadratic function.
03

Determine the best fit model

In our case, after plotting each data point from the table, we see that they all lie along a straight line. This indicates a linear relationship, Thus, the graph represents a linear function. This is also confirmed by the fact that with each increase by 1 in x-value, the y-value increases by 5, which is a characteristic of a linear function.

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Most popular questions from this chapter

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In Exercises 1-22, graph each linear inequality. \(x+y \geq 2\)

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