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 greater population at the
18-hour mark?

Culture A: 900, 1350, 2025, 3037.5.
Culture B: 10, 20, 40, 80

A. Culture A

B. Culture B​

Answer 1

the answer is Culture B :)

Answer 2

Culture B

Explanation:

In Culture A, the number of bacteria is increasing in a G.P. sequence with first term 900 and common ratio 1.5.

Therefore, the 18th-hour population of bacteria will be

`900 * (1.5)^((18 - 1)) = 886735.128`

Again in Culture B, the number of bacteria is increasing in a G.P. sequence with first term 10 and common ratio 2.

Therefore, the 18th-hour population of bacteria will be

`10(2)^((18 - 1)) = 1310720`

Therefore, Culture B will have a greater population at the 18-hour mark. (Answer)