Edexcel Mathematics October 2021 · Paper 1 · Question 8 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

October 2021 · Paper 1 · Question 8 · 9 marks

8. A scientist is studying the growth of two different populations of bacteria. The number of bacteria, N, in the first population is modelled by the equation N = Aekt t  0 where A and k are positive constants and t is the time in hours from the start of the study. Given that • there were 1000 bacteria in this population at the start of the study • it took exactly 5 hours from the start of the study for this population to double (a) find a complete equation for the model. (4) (b) Hence find the rate of increase in the number of bacteria in this population exactly 8 hours from the start of the study. Give your answer to 2 significant figures. (2) The number of bacteria, M, in the second population is modelled by the equation M = 500e1.4kt t  0 where k has the value found in part (a) and t is the time in hours from the start of the study. Given that T hours after the start of the study, the number of bacteria in the two different populations was the same, (c) find the value of T. (3) 23 24 25

Lesson: Exponential Functions and Their Graphs