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10 October, 06:47

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, ...

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  1. 10 October, 09:35
    0
    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.
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