- PRE - CALCULUS

Question

Consider how a rumor might spread among a population. Suppose on Day 1 a single person

tells someone else a rumor, and suppose that on every subsequent day, each person who knows

the rumor tells exactly one other person the rumor.

a) How many days until 50 people have heard the rumor?

b) How many days until 100 people have heard the rumor?

Answer 1

Fibonnaci!

1, 1, 2, 3, 5, 8, 13, 21, 54

Answer 2

a) N = 2^{n -1} = 50; n = [ln50/ln2] + 1 = 7

b) On next day, so n = 8