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28 June, 14:09

A bacteria culture has an initial population of 25. This bacteria reproduces at a daily rate of 1.28 percent. How long will it take for the population to grow to 375 bacteria?

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  1. 28 June, 14:20
    0
    211 days
  2. 28 June, 14:31
    0
    212.9 days

    Step-by-step explanation:

    The bacteria culture initial population is 25 represented by Po and the population after t days is represented by P (t).

    Using growth formula:

    P (t) = Po (1 + r) ^t where r is rate in percent and t is time in days

    r = 1.28%, P (t) = 375, and Po = 25

    substituting this values into the equation above yields

    375 = 25 (1 + 1.28/100) ^t

    375:25 = (1 + 0.0128) ^t

    15 = (1.0128) ^t

    take logarithm of both sides

    log 15 = log (1.0128) ^t remember the law log a^b = b log a

    applying the same law gives

    log 15 = t log 1.0128

    divide both side by log 1.0128

    log 15 : log 1.0128 = t log 1.0128 : log 1.0128

    t = 212.9 days
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