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AP Calculus AB Cha 3 C Interpret Rates of Change in Applied Contexts Questions

Practise applied rates-of-change questions by interpreting derivatives in context and matching units and signs to the situation.

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

AP Calculus AB Cha 3 C Interpret Rates of Change in Applied Contexts Questions 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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