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(a) The number of atoms of a strange element on Earth per hour is the average of

ID: 3833130 • Letter: #

Question

(a) The number of atoms of a strange element on Earth per hour is the average of the number of atoms in two previous hours. Assume that there were 100,000 atoms in hour 1 and 300,000 atoms in hour 2. Construct a recurrence relation for the number of atoms in hour n. State two initial conditions. (b) Suppose that in a bookshop every month fifty new copies of a book are added for each book that was present the previous month, and that all books that are 2 months old are removed. The bookshop starts with five new books. Set up a recurrence relation for the number of books present after n months. State two initial conditions.

Explanation / Answer

a)

NOOFATOM(t)= 100000 when t =1

NOOFATOM(t)= 300000 when t =2

NOOFATOM(t)= [ NOOFATOM(t-1) + NOOFATOM (t-2) ] /2 ….when t >2

b)

NOOFBOOKS(n)= 5 when n=1

NOOFBOOKS(n)= 5*50 = 250 when n=2

NOOFBOOKS(n)= 50 *NOOFBOOKS(n-1) - NOOFBOOKS(n-2) when n>3