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23 April, 03:23

The amount of bacteria in a petri dish increases at a rate proportional to the amount present. At time t=0, the amount of bacteria in the dish is 10 grams. At time t=2, the amount of bacteria in the dish is 30 grams. What is the amount of bacteria in the dish at time t=6?

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  1. 23 April, 03:51
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    Step-by-step explanation:

    Formula to be used is N=N0e^ (kt)

    N0 - amount of bacteria at time 0, which is 10g

    t=2, 30g

    30 = 10*e^ (k*2)

    3 = e^ (2k)

    2k = ln3

    k = 0.5ln3

    At t=6:

    N = 10*e^ (0.5ln3*6)

    N = 10e^ (3ln3)

    N = 10e^ln27

    N = 10*27 = 270

    So the amount of bacteria at t=6 is 270
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