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a. Make a scatter plot of the data in the table below.

b. Does it appear that a linear model or an exponential model is the better fit for the​ data?
                                                                                             
x
1
2
3
4
5
6
y
9.8
13.7
19.2
26.9
37.6
52.7
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Part 1
a. Choose the scatter plot below.
A.
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A scatterplot has a horizontal x-axis labeled from 0 to 55 in increments of 5 and a vertical y-axis labeled from 0 to 55 in increments of 5. Points are plotted at (9.8, 9.8), (13.7, 13.7), (19.2, 19.2), (26.9, 26.9), (37.6, 37.6), and (52.7, 52.7). All coordinates are approximate.
B.
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A scatterplot has a horizontal x-axis labeled from 0 to 55 in increments of 5 and a vertical y-axis labeled from 0 to 6 in increments of 1. Points are plotted at (9.8, 1), (13.7, 2), (19.2, 3), (26.9, 4), (37.6, 5), and (52.7, 6). All coordinates are approximate.
C.
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1 answer

To analyze the data you provided and generate a scatter plot, let’s summarize the steps required for both parts of your question.

Part 1: Scatter Plot

The data from your table is as follows:

| x | y | |---|------| | 1 | 9.8 | | 2 | 13.7 | | 3 | 19.2 | | 4 | 26.9 | | 5 | 37.6 | | 6 | 52.7 |

The scatter plot should depict the relationship between the values of x and y.

Choosing the Correct Scatter Plot from Options:

  1. Option A:

    • Contains points (9.8, 9.8), (13.7, 13.7), etc.
    • This is incorrect because the y-values and x-values are not paired correctly.

  2. Option B:

    • Contains points such as (9.8, 1), (13.7, 2), etc.
    • This is incorrect since it does not reflect the correct y-values for each x-value.

  3. Option C:

    • This option does not provide data points but appears to indicate it will plot them correctly as labeled.
    • Without specific points displayed, it's hard to verify, but it might be the best representation if it actually uses the correct coordinates.

Since I can't physically plot the graph here, use the data points above to plot (x, y) pairs as follows:

  • (1, 9.8)
  • (2, 13.7)
  • (3, 19.2)
  • (4, 26.9)
  • (5, 37.6)
  • (6, 52.7)

Part 2: Model Fit Evaluation

To determine if a linear or exponential model fits better, we look at the trend in the points:

  • Linear Model: Represents a constant rate of change. If the increase in y-values is approximately the same for equal increments in x, a linear model is appropriate.
  • Exponential Model: Characterizes growth that increases at a percentage. If the y-values increase increasingly larger amounts as x increases (not constant), an exponential model is likely a better fit.

Analysis of the Given Data:

  • The differences between the y-values are not constant:
    • From y(1) to y(2): 13.7 - 9.8 = 3.9
    • From y(2) to y(3): 19.2 - 13.7 = 5.5
    • From y(3) to y(4): 26.9 - 19.2 = 7.7
    • From y(4) to y(5): 37.6 - 26.9 = 10.7
    • From y(5) to y(6): 52.7 - 37.6 = 15.1
  • The increasing differences indicate an exponential growth pattern, since the increase in y becomes progressively larger as x increases.

Conclusion:

  1. The correct scatter plot would show the points (1, 9.8), (2, 13.7), (3, 19.2), (4, 26.9), (5, 37.6), (6, 52.7).
  2. The data appears to fit an exponential model better than a linear model based on the increasing differences between y-values.