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21 March, 17:10

A broth containing 1 million bacterial cells is treated with an antimicrobial agent that kills 90% of the cells in 1 minute. what is the minimum amount of time it will take before all the cells in the broth are dead?

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  1. 21 March, 18:32
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    The answer is 7 minutes.

    After 1 minute:

    1,000,000 - 90% * 1,000,000

    = 1,000,000 - 0.9 * 1,000,000

    = 1,000,000 - 900,000

    = 100,000

    After 2 minutes:

    100,000 - 90% * 100,000

    = 100,000 - 0.9 * 100,000

    = 100,000 - 90,000

    = 10,000

    After 3 minutes:

    10,000 - 90% * 10,000

    = 10,000 - 0.9 * 10,000

    = 10,000 - 9,000

    = 1,000

    After 4 minutes:

    1,000 - 90% * 1,000

    = 1,000 - 0.9 * 1,000

    = 1,000 - 900

    = 100

    After 5 minutes:

    100 - 90% * 100

    = 100 - 0.9 * 100

    = 100 - 90

    = 10

    After 6 minutes:

    10 - 90% * 10

    = 10 - 0.9 * 10

    = 10 - 9

    = 1

    After 7 minutes:

    1 - 90% * 1

    = 1 - 0.9 * 1

    = 1 - 0.9

    = 0.1

    Since 0.1 is not a whole bacterial cell, 7 minutes are enough to kill all bacterial cells.
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