An environmental scientist observes that the concentration C (in milligrams per liter) of a particular algae species in a lake changes over time t (in days). The scientist’s field notes include the statement:
“The instantaneous rate of change of algae concentration is proportional to the current concentration.”
Assume no other factors influence the growth of the algae population during the observation period.
(1) Identify the dependent and independent variables for this situation and specify appropriate units for each.
(2) Write a differential equation that mathematically represents the scientist’s statement. Clearly define any parameters you introduce.
(3) Describe, in complete sentences, the practical meaning of each term in your differential equation, including correct units.
(4) Without solving the differential equation, determine the sign of the proportionality constant and justify your conclusion in the context of algae growth.