Question

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

x y
2 4.4
7 18.2
13 120.0
19 715.4
22 1,768.3
26 5,775.9
30 10,508.5
When x = 13, what is the second coordinate in a scatterplot of the linearized data? Round your answer to the tenths place.

(1 point)
Responses

0.3
0.3

2.1
2.1

58.1
58.1

120.0

Answer 1

To linearize the data from the scatterplot, we can take the logarithm of the y-values. This is often done when the relationship between x and y is exponential.

Given the data:
- For \( x = 13 \), the corresponding \( y \) value is \( 120.0 \).

We'll calculate the natural logarithm (or common logarithm) of the \( y \) value \( 120.0 \).

Using a calculator to find \( \log_{10}(120.0) \):

\[
\log_{10}(120.0) \approx 2.079
\]

Rounding this to the tenths place, we get:

\[
\log_{10}(120.0) \approx 2.1
\]

Therefore, when \( x = 13 \), the second coordinate in the scatterplot of the linearized data is approximately **2.1**.

Hence, the correct response is:

**2.1**