Sand is being deposited along a stretch of shoreline
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Sand is being deposited along a stretch of shoreline. The rate, in cubic feet per minute, at which sand is added at time t minutes after the start of monitoring is modeled for 0≤t≤20 by
R(t)=0.2t2−3t+40.
Define F(t) to be the accumulated volume of sand (in cubic feet) deposited from the start of monitoring up to time t minutes, so that F(0)=0.
Answer the following questions about this situation.
(a) Explain the practical meaning of F(15) in the context of the problem. Include units in your answer.
(b) Compute F′(10) and interpret its value, including appropriate units.
(c) Determine the exact value of F(20). State whether the shoreline gained or lost sand over the interval and justify your answer.
(d) Determine the average rate at which sand is deposited over the first 20 minutes and describe how this average compares to the instantaneous rate at t=0. Justify your conclusion.