OCR MEI C3 2012 June — Question 5

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2012
SessionJune
TopicExponential Functions

5 A termites' nest has a population of \(P\) million. \(P\) is modelled by the equation \(P = 7 - 2 \mathrm { e } ^ { - k t }\), where \(t\) is in years, and \(k\) is a positive constant.
  1. Calculate the population when \(t = 0\), and the long-term population, given by this model.
  2. Given that the population when \(t = 1\) is estimated to be 5.5 million, calculate the value of \(k\).