AP Calculus AB Unit 7.3: Slope Fields

Practice AP Calculus Unit 7.3 questions on sketching solution curves through slope fields and estimating differential-equation behavior.

Exam points

sketch a solution curve through a slope field while following the given point and local slope directions
use a slope field to estimate the behavior of solutions to a first-order differential equation

Covered syllabus points

FUN-7.C—Estimate solutions to differential equations

[Maximum number: 1]

The depth of seawater at a location can be modeled by the function H that satisfies the differential equation $\frac{d H}{d t}=\frac{1}{2}(H-1) \cos \left(\frac{t}{2}\right)$ , where H(t) is measured in feet and t is measured in hours after noon ( t=0 ). It is known that H(0)=4.

A portion of the slope field for the differential equation is provided. Sketch the solution curve, y=H(t), through the point (0, 4).

Figure for Question 7.3 Sketching Slope Fields question 1 — AP Calculus AB

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Covered syllabus points

7.3 Sketching Slope Fields question 1