Ask a New Question
Menu

Use the graphing tool at the right to create a scatter plot for the data in the table. 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.

x
y
0
0
4
0.6
9
1.0
17
1.2
23
1.4
Part 2
Plot each​ point, one at a time. Using the graphing​ tool, start by plotting ​(0,0).
.
.
.
Question content area right
Part 1
-6
-3
3
6
9
12
15
18
21
24
27
-0.6
-0.3
0.3
0.6
0.9
1.2
1.5
1.8
x
y

1 answer

To create a scatter plot for the provided data set, we'll start by plotting each point one at a time, as you instructed. Here’s the data again for reference:

| x | y | |----|-----| | 0 | 0 | | 4 | 0.6 | | 9 | 1.0 | | 17 | 1.2 | | 23 | 1.4 |

Now let's plot the points step-by-step:

  1. Plot (0, 0): This is the origin of the plot, where both x and y values are 0.
  2. Plot (4, 0.6): This point is to the right of (0, 0) along the x-axis and slightly above it.
  3. Plot (9, 1.0): This point is further to the right on the x-axis and at 1.0 on the y-axis.
  4. Plot (17, 1.2): This point continues right on the x-axis and remains slightly above 1.0 on the y-axis.
  5. Plot (23, 1.4): This point is also further to the right and continues the upward trend, reaching 1.4 on the y-axis.

Shape of the Scatter Plot:

Once you plot all these points, you can look at their overall arrangement to identify the trend.

From the values:

  • As \( x \) increases, \( y \) increases, but the rate of increase appears to be slowing down (i.e., the increase in \( y \) is less than proportional to the increase in \( x \)).

Analysis:

  • Linear Function: Displays a constant rate of increase, which doesn't match our data.
  • Exponential Function: Shows rapid growth, which also does not match the data.
  • Logarithmic Function: Could be a candidate if the data level off significantly.
  • Quadratic Function: Might fit if there is a parabolic trend, which does not appear evident here.

Conclusion:

Based on the provided data points, the relationship seems to have a gradual increase that suggests a logarithmic or possibly quadratic function, but it is weaker than either. Notably, if we assume the data continues to form a clear increasing trend that slows down, a logarithmic function could be the best fit; however, further analysis with more data points or regression analysis would solidify the conclusion.

To visualize this accurately, you could utilize graphing software, a calculator, or tools like Desmos or GeoGebra to confirm the best fit for the line through regression analysis.