page 04 MARKS 3. E,ABCD is a rectangular based pyramid. AB = p, AD = q and AE = r. F C B E D p r q A (a) Express BE in terms of p and r. Point F divides BC in the ratio 3:1. (b) Express vector EF in terms of p, q and r. 4. In a forest, the population of a species of mouse is falling by 2·7% each year. To increase the population scientists plan to release 30 mice into the forest at the end of March each year. (a) un is the estimated population of mice at the start of April, n years after the population was first estimated. It is known that un and un+1 satisfy the recurrence relation 1 n n u au b + = + . State the values of a and b. The scientists continue to release this species of mouse each year. (b) (i) Explain why the estimated population of mice will stabilise in the long term. (ii) Calculate the long term population to the nearest hundred. 1 2 1 1 2