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AP Calculus AB 4.3 Applied Rates Review

Review AP Calculus AB 4.3 by translating derivatives into rates with correct units and signs, then interpreting what the value means in an applied setting.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • interpret the meaning and units of a derivative in context
  • use signs and values of rates of change to explain an applied situation

Covered syllabus points

CHA-3.C—Interpret rates of change in applied contexts

4.3 Rates of Change in Applied Contexts Other Than Motion question 1

[Maximum number: 4]

When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove

bananas from the display table at a rate modeled by

f(t)=10+(0.8t)sin⁡(t3100) for 0<t≤12,f(t)=10+(0.8 t) \sin \left(\frac{t^{3}}{100}\right) \text { for } 0<t \leq 12,

where f(t) is measured in pounds per hour and t is the number of hours after the store opened. After the

store has been open for three hours, store employees add bananas to the display table at a rate modeled by

g(t)=3+2.4ln⁡(t2+2t) for 3<t≤12,g(t)=3+2.4 \ln \left(t^{2}+2 t\right) \text { for } 3<t \leq 12,

where g(t) is measured in pounds per hour and t is the number of hours after the store opened.

Question (a)

(a)

Find f′(7)f^{\prime}(7). Using correct units, explain the meaning of f′(7)f^{\prime}(7) in the context of the problem.

[ 2 ]

Question (b)

(b)

Is the number of pounds of bananas on the display table increasing or decreasing at time t=5 ? Give a

reason for your answer.

[ 2 ]
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