Answer:
1) Recursive definition:
2) At the beginning of the 4th interval
Explanation:
1)
The initial population of the bacteria at time zero is
Here we are told that the reading is taken every two hours; we call this time interval "n", so
And also, after every time interval n, the number of bacteria has tripled.
This means that when n = 1,
And when n=2,
Applied recursively, we get
And substituting p0,
(1)
2)
Here we want to find at the beginning of which interval there are
bacteria.
This means that we can rewrite eq.(1) as
By simplifying,
Which means that
However, this means that the number of bacteria is 1,350,000 after 3 time intervals; therefore, at the beginning of the 4th interval.