Question

Write a recursive formula for each sequence given or described below.

. A bacteria culture has an initial population of 10 bacteria, and each hour the population triples in size

Answer 1

Recursive form is number of bacteria after n hours b(n) = 3 x b(n-1), where b(0) = 10 and n ≥ 1

Explanation:

Let b(n) be the number of bacteria after n hours.

We have b(0) = 10

Given that each hour the population triples in size

That is

b(1) = 3 x 10 = 3b(0)

b(2) = 3 x b(1)

b(3) = 3 x b(2)

b(n) = 3 x b(n-1)

Recursive form is number of bacteria after n hours b(n) = 3 x b(n-1), where b(0) = 10 and n ≥ 1