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

Question

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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Samantha 3 weeks 2021-10-10T19:47:05+00:00 2 Answers 0

Answers ( )

    0
    2021-10-10T19:48:24+00:00

    Answer:

    211 days

    Step-by-step explanation:

    0
    2021-10-10T19:48:26+00:00

    Answer:

    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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