CAIE P3 2011 November — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2011
SessionNovember
TopicFirst order differential equations (integrating factor)

4 During an experiment, the number of organisms present at time \(t\) days is denoted by \(N\), where \(N\) is treated as a continuous variable. It is given that $$\frac { \mathrm { d } N } { \mathrm {~d} t } = 1.2 \mathrm { e } ^ { - 0.02 t } N ^ { 0.5 }$$ When \(t = 0\), the number of organisms present is 100 .
  1. Find an expression for \(N\) in terms of \(t\).
  2. State what happens to the number of organisms present after a long time.