Answer :
Option(b) is correct because it accurately represents the linear increase in pressure with depth based on the given data points.
The given problem states that the pressure increases linearly as the scientist descends into the saltwater. This implies a constant rate of change in pressure with respect to depth. We can use the two provided data points to determine the linear relationship. The first data point is (9, 18.7) and the second data point is (14, 20.9).
For the linear model, we need to determine the slope [tex](\(m\))[/tex] and the y-intercept [tex](\(b\))[/tex] of the equation [tex]\(p = md + b\).[/tex] The slope represents the rate of change of pressure with depth, and the y-intercept corresponds to the initial pressure at zero depth.
Using the two data points:
[tex]Slope (\(m\)) = \(\frac{{20.9 - 18.7}}{{14 - 9}} = 0.44\)[/tex]
Substitute the slope into one of the data points to find the y-intercept [tex](\(b\))[/tex]:
[tex]\(18.7 = 0.44 \times 9 + b\)[/tex]
[tex]\(b = 14.74\)[/tex]
So the linear model that describes the pressure [tex]\(p\)[/tex] in pounds per square inch at a depth [tex]\(d\)[/tex] feet below the surface is [tex]\(p = 0.44d + 14.74\).[/tex]
Therefore,the correct option is (b).
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