Edexcel Mathematics June 2018 · Paper 2 · Question 14 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

June 2018 · Paper 2 · Question 14 · 10 marks

14. A scientist is studying a population of mice on an island. The number of mice, N, in the population, t months after the start of the study, is modelled by the equation N = 900 37025+−e.t, t ∈ , t  0 (a) Find the number of mice in the population at the start of the study . (1) (b) Show that the rate of growth d dN t is given by d dN t = NN()300 1200− (4) The rate of growth is a maximum after T months. (c) Find, according to the model, the value of T. (4) According to the model, the maximum number of mice on the island is P. (d) State the value of P . (1) 43 44

Lesson: Exponential Functions and Their Graphs