Question

A culture of bacteria doubles every 2 hours. Is the bacteria growth over time an arithmetic or geometric sequence? Why?

Answer 1

A culture of bacteria doubles every 2 hours.  If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

Is this sequence arithmetic or geometric?

What is the initial term?

What is the rate of change (common ratio or common difference)?

Solution: There are 500 bacteria to start, doubling every 2 hrs..

Such bacterial growth is a geometric sequence with a common ratio of 2. 

The number of times the bacteria doubles is 12 times during a 24 hour period.

The starting number is 500 and the common ratio is 2 hours.   The total number of bacteria is 2,048,000.

Determine if the sequence is geometric.  If it is, find the common ratio.

9).  - 1, - 6, - 36, 216, ...... Geometric - Yes, Common Ratio is - 6

9). - 1, - 1,  4,  8,......  Geometric - No

10). 4, 16, 36, 64, ..... Geometric - No

10). - 3, - 15, - 75, - 375,......Geometric - Yes, Common Ratio is 5

11). - 2, - 4, - 8, - 16,...... Geometric - Yes,  Common Ratio is 2

11). 1, 5, 25, - 125,...... Geometric - Yes, Common Ratio is - 5

Hope this helps!!!!!