AP Calculus AB 4.3 Rates of Change in Applied Contexts Question Bank

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

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

[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+(0.8 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+2.4 \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.

(a)

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

[ 2 ]

$f^{\prime}(7)=-8.120$ (or -8.119)

After the store has been open 7 hours, the rate at which bananas are

being removed from the display table is decreasing by 8.120 (or 8.119)

pounds per hour per hour.

(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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CHA-3.C—Interpret rates of change in applied contexts question 1

Question (a)

Question (b)