Question

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, ...

Answer 1

Every hour, A is increased by 1.5 times, and B is doubled.
Using this we can say that
A(t) = 800 * (1.5)^(t-1)
B(t) = 5 * (1.5)^(t-1)
Where A(t) is the size of colony A at time t and B(t) is the size of colony B at time t.

Answer 2

so my answer is A! thanks!