MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Two species of algae, X and Y, each satisfy dtdN=kN in identical laboratory conditions. For species X, the population increases from 500 cells to 800 cells in 6h. For species Y, the population grows from 400 cells to 700 cells in the same 6h interval.
(1) Part 1: (a) Without solving explicitly for either population function, determine which species has the larger growth constant. Justify your answer verbally or symbolically.
(2) Part 2: (b) Explain why knowledge of any two distinct population measurements taken at known times is sufficient to determine the unique value of k for either species.