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

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

b) If 100 bacteria are used to begin a new colony, how many bacteria will be in the colony in 10 hours?

Solution

Step 1:

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

In this problem in part (a) we have to set up a recurrence relation from the given information for the number of bacteria after n hours have elapsed.

And in part (b) we have to find the number of bacteria in 10 hours if 100 bacteria are used to begin a new colony.