## nab recurrence relation question

### catmandoo

Posted 16 October 2010 - 01:06 PM

the question- in a wood one fifth of the existing birds are killed by predators each year but during the nesting session 600 chicks are hatched . there are un birds at the start of a particular year

(a) write down a recurrence relation for un+1, the number of birds at the start of the next year
(b) find the limit of the sequence generated by this recurrence relation and explain what the limit means in the context of this question

### Physics and Maths Tutor

Posted 16 October 2010 - 08:30 PM

catmandoo, on 16 October 2010 - 01:06 PM, said:

the question- in a wood one fifth of the existing birds are killed by predators each year but during the nesting session 600 chicks are hatched . there are un birds at the start of a particular year

(a) write down a recurrence relation for un+1, the number of birds at the start of the next year
(b) find the limit of the sequence generated by this recurrence relation and explain what the limit means in the context of this question

un+1 = mun + c
killed = 1/5 = 0.2
so, m = 0.8
c=600
a) un+1 = 0.8un + 600
b) L = c/(1-m) = 600/(1-0.8) = 600/0.2 = 3000
one fifth of 3000 =3000/5 = 600 (killed every year)
but 600 born every year

Physics & Maths Tutor
tutor@physics-maths.co.uk
www.physics-maths.co.uk