OCR C4 — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
TopicDifferential equations

8. A small town had a population of 9000 in the year 2001. In a model, it is assumed that the population of the town, \(P\), at time \(t\) years after 2001 satisfies the differential equation $$\frac { \mathrm { d } P } { \mathrm {~d} t } = 0.05 P \mathrm { e } ^ { - 0.05 t }$$
  1. Show that, according to the model, the population of the town in 2011 will be 13300 to 3 significant figures.
  2. Find the value which the population of the town will approach in the long term, according to the model.