The following geometric sequences represent the populations of two bacterial cultures at the 1-hour mark, the 2-hour mark, the 3-hour mark, and so on. Culture A starts with more bacteria, but culture B has a ratio of increase that is larger. Which culture will have the greatest population at the 19-hour mark?

A. 800, 1,200, 1,800, 2,700, ...

B. 5, 10, 20, 40, ...

The explicit formula for geometric sequence is given by:

a (n) = a (1) r^ (n-1)

Where,

a (n) = population after time n

a (1) = population at the start

r = common ratio

For bacteria A;

a (1) = 800

r = 120/800 = 1800/1200 = 2700/1800 = 1.5

Then, after 19 hours;

a (19) = 800*1.5^ (19-1) = 1182313.504 ≈ 1182314

Fro bacteria B;

a (1) = 5

r = 10/5 = 20/10 = 40/20 = 2

Then, after 19 hours;

a (19) = 5*2^ (19-1) = 1310720

Therefore, culture B will have a greater population after 19-hour mark.