8 P72118A 8. The owner of a new company models the number of customers that the company will have at the end of each month. The owner assumes that • a constant proportion, p (where 0 < p < 1), of the previous month’s customers will be retained for the next month • a constant number of new customers, k, will be added each month. Let un (where n  1) represent the number of customers that the company will have at the end of n months. The company has 5000 customers at the end of the first month. (a) By setting up a first order recurrence relation for un + 1 in terms of un, determine an expression for un in terms of n, p and k. (6) The owner believes that 95% of the previous month’s customers will be retained each month and that there will be 10 000 new customers each month. According to the model, the company will first have at least 135 000 customers by the end of the mth month. (b) Using logarithms, determine the value of m. (3) (Total for Question 8 is 9 marks) TOTAL FOR PAPER IS 75 MARKS Centre Number Candidate Number Turn over Total Marks Candidate surname Other names Please check the examination details below before entering your candidate information Paper reference Answer Book Do not return the question paper with the answer book. Further Mathematics Advanced PAPER 4D: Decision Mathematics 2 Time 1 hour 30 minutes 9FM0/4D Pearson Edexcel Level 3 GCE P72118A ©2022 Pearson Education Ltd. 1/1/1/ 2 1. 1 2 3 4 A 32 45 34 48 B 37 39 50 46 C 46 44 40 42 D 43 45 48 52 You may not need to use all of these tables. 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D 1 2 3 4 A B C D _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________