MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A river carries dissolved pollutant downstream. At a monitoring station the concentration, in milligrams per liter, is modeled by
C(t)=0.1t2−t+5,
and the volumetric flow rate, in liters per minute, is modeled by
Q(t)=400+10sin(6πt),
where t is the time in minutes since midnight. Consider the time interval 0≤t≤12 minutes.
(a) Write an expression M(t) for the instantaneous rate, in milligrams per minute, at which pollutant mass passes the station at time t. Simplification is not required.
(b) Determine the total mass of pollutant (in milligrams) that passes the station during the 12-minute interval. Show all steps of your calculation.
(c) Compute the average mass transport rate (in milligrams per minute) over 0≤t≤12 and explain how it compares to M(0). Provide justification based on your work in part (b).