During a 4-hour storm

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

During a 4-hour storm, the instantaneous rainfall rate (in inches per hour) RR is modeled for 0≤t≤40\le t\le4 by R(t)=0.015t2+0.20t+1.00,R(t)=0.015t^{2}+0.20t+1.00, where tt is measured in hours since the storm began. (1) Calculate the average rainfall rate during the storm. (2) Determine the total depth of rain that fell during the 4-hour period by using the average rate from part (a). Then verify that this result equals the value of ∫04R(t) dt\int_{0}^{4}R(t)\,dt.

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