math

A colony of bacteria is growing exponentially, increasing in size from 200 to 500 cells in 100 minutes will it take the colony to double in size?

asked by Patty
  1. p = ae^kt
    500 = 200e^100k
    2.5 = e^100k
    ln 2.5 = 100k
    k = ln2.5/100

    p = 200e^(ln2.5/100 t)
    = 200*2.5^t/100

    to double,
    2 = 2.5^t/100
    ln 2 = (t/100)ln2.5
    t = 100 * ln2/ln2.5 = 75.65 minutes

    posted by Steve

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