The population P of a town decreases at a rate proportional to the number by which the population exceeds 1000, proportionality constant being `k gt 0`. Find (a) Population at any time t, given initial population of the town being 2500. (b) If 10 years later the population has fallen to 1900, find the time when the population will be 1500. (c) Predict about the population of the town in the long run.

Answer

a) P = 1000 + 1500 `e^–kt where k = 1/10 ln (5/3)`; (b) `T = 10 log_5/3 (3)`; ( c) P = 1000 as t `Rightarrow infty`