Bacterial growth problem?

It is noon and we start with 1 bacteria which divides every minute. In 47 minutes, the petri dish is half covered in bacteria. Write an equation that expresses the growth rate. How long did it take for 1/3 of the petri dish to be covered in bacteria?

Update:

Ok, I saw that I had to use P=AB^t, but I couldn't figure out what B was. How did you get 2 for B?

Comments

  • P = A * 2^t

    t is in minutes

    A = 1

    P = 1 * 2^47

    So, when P = 2^47, the dish is half full

    The dish is 1/3 full when P = (2/3) * 2^47

    (2/3) * 2^47 = 2^t

    2^48 / 3 = 2^t

    ln(2^48 / 3) = t * ln(2)

    ln(2^48) - ln(3) = t * ln(2)

    t = (48 * ln(2) - ln(3)) / ln(2)

    t = 46.415037499278843818546261056052

    46 minutes, 25 seconds

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