Environmental scientists monitoring Bluewater Lake record the concentration (in mg/L)…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Environmental scientists monitoring Bluewater Lake record the concentration C (in mg/L) of a soluble pollutant. At noon (t=0 h), the concentration is 12.0 mg/L, and field instruments report an instantaneous rate of change of −0.35 mgL−1h−1 at that same moment.
(a) Interpret the numerical value −0.35 mgL−1h−1 in the context of the scenario, stating the meaning of both the sign and the units.
(b) Describe qualitatively what is expected to happen to the pollutant concentration during the hour immediately following noon.
(c) Explain why the derivative alone does or does not suffice to predict the exact concentration at t=3 h. State any additional information that would be required for a reliable prediction.