Question

Suppose a scatterplot is created from the points in the following table.

x y
1 38.4
3 54.6
6 96.9
7 112.8
10 199.5
14 411.3
16 591.6
When x = 7, what is the second coordinate in a scatterplot of the linearized data? Round your answer to the tenths place.

(1 point)
Responses

0.8
0.8

2.1
2.1

54.3
54.3

112.8

Answer 1

To create a linearized scatterplot, we typically transform the data in some way to achieve a linear relationship. In this case, it looks like the y-values are not linear. One common technique for linearizing data is to take the logarithm of the y-values.

Given the values in the table, let's calculate the logarithm (base 10 for simplicity) of the y-values, as follows:

1. For \( x = 1, y = 38.4 \): \( \log_{10}(38.4) \approx 1.584 \)
2. For \( x = 3, y = 54.6 \): \( \log_{10}(54.6) \approx 1.737 \)
3. For \( x = 6, y = 96.9 \): \( \log_{10}(96.9) \approx 1.986 \)
4. For \( x = 7, y = 112.8 \): \( \log_{10}(112.8) \approx 2.052 \)
5. For \( x = 10, y = 199.5 \): \( \log_{10}(199.5) \approx 2.301 \)
6. For \( x = 14, y = 411.3 \): \( \log_{10}(411.3) \approx 2.614 \)
7. For \( x = 16, y = 591.6 \): \( \log_{10}(591.6) \approx 2.773 \)

Now, for \( x = 7 \), the second coordinate in the scatterplot of the linearized data \( \log_{10}(112.8) \) is approximately 2.052.

Rounding to the tenths place, we find that it is:

**2.1**

Thus, the answer is:

**2.1**