A study models the total mass (in kilograms) of a pollutant that has accumulated in a…
MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
A study models the total mass P(x) (in kilograms) of a pollutant that has accumulated in a lake after x days. The rate at which the pollutant enters the lake is r(t) kilograms per day, where r is continuous and positive for t≥0. The model is given by
P(x)=∫0x2r(t)dt.
Answer the following questions about this model.
(a) Describe, in the context of the scenario, the practical meaning of P′(x). Include appropriate units in your description.
(b) Suppose that r(t) is an increasing function. Determine whether P′(x) is increasing, decreasing, or neither for x>0, and justify your conclusion using properties of the function r.