Edexcel Mathematics June 2023 · Paper 2 · Question 12 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

June 2023 · Paper 2 · Question 12 · 10 marks

12. O5tN NA NB Figure 2 The number of subscribers to two different music streaming companies is being monitored. The number of subscribers, NA , in thousands, to company A is modelled by the equation NA = |t – 3| + 4 t  0 where t is the time in years since monitoring began. The number of subscribers, NB , in thousands, to company B is modelled by the equation NB = 8 – |2t – 6| t  0 where t is the time in years since monitoring began. Figure 2 shows a sketch of the graph of NA and the graph of NB over a 5-year period. Use the equations of the models to answer parts (a), (b), (c) and (d). (a) Find the initial dif ference between the number of subscribers to company A and the number of subscribers to company B. (2) When t = T company A reduced its subscription prices and the number of subscribers increased. (b) Suggest a value for T, giving a reason for your answer. (2) (c) Find the range of values of t for which NA > NB giving your answer in set notation. (5) (d) State a limitation of the model used for company B. (1) 35