Kenneth Rosen:Advance Counting Technique

Question

11)Suppose that the number of bacteria in a colony triples every hour.

1. Set up a recurrence relation for the number of bacteria after n hours have elapsed

2. If $100$ bacteria are used to begin a new colony, how many bacteria will be  in colony  in 10 hours

Answer 1

 a)an = 3an-1 

where an is the number of bacteria after n hours,

b)$a_{10}=3.a_{9}$

$\Rightarrow a_{10}=3^{10}.a_{0}$

$\Rightarrow a_{10}=3^{10}.100=5904900$

Answer 2

a_n = 3ⁿ