M:C:MC:15

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When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

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$p equals 0.44 d plus 0.77$

Correct Answer:

$p equals 0.44 d plus 14.74$

Correct Answer:

Yes

$p equals 2.2 d minus 1.1$

Correct Answer:

$p equals 2.2 d minus 9.9$

Correct Answer:

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Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives $fraction numerator 20.9 minus 18.7 over denominator 14 minus 9 end fraction space equals space fraction numerator 2.2 over denominator 5 end fraction comma$ or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation $18.7 space equals space 0.44 left parenthesis 9 right parenthesis space plus space b$ gives $b space equals space 14.74.$ Therefore, the model that can be used to relate the pressure and the depth is $p space equals space 0.44 d space plus space 14.74.$

Choice A is not the correct answer. The rate is calculated correctly, but the student may have incorrectly used the ordered pair $left parenthesis 18.7 comma space 9 right parenthesis$ rather than $left parenthesis 9 comma space 18.7 right parenthesis$ to calculate the pressure at a depth of 0 feet.

Choice C is not the correct answer. The rate here is incorrectly calculated by subtracting 20.9 and 18.7 and not dividing by 5. The student then uses the coordinate pair $d space equals space 9$ and $p equals 18.7$ in conjunction with the incorrect slope of 2.2 to write the equation of the linear model.

Choice D is not the correct answer. The rate here is incorrectly calculated by subtracting 20.9 and 18.7 and not dividing by 5. The student then uses the coordinate pair $d space equals space 14$ and $p space equals space 20.9$ in conjunction with the incorrect slope of 2.2 to write the equation of the linear model.

Question Difficulty:

medium

Objective:

Students must construct a linear equation to represent a real-world situation.

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Question 19 of 30

M:C:MC:15

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