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Question 19 of 30

beginning of content:

M:C:MC:15

Tags:
SAT

Exam

PSAT/NMSQT

Exam

PSAT 10

Exam

Calculator: Permitted
Heart of Algebra

Subscore

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?

No

Yes

No

No

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  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  gives  Therefore, the model that can be used to relate the pressure and the depth is

Choice A is not the correct answer. The rate is calculated correctly, but the student may have incorrectly used the ordered pair  rather than  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  and  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  and  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.