In a lab experiment, 100 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double ev

Question

In a lab experiment, 100 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 13 hours. How long would it be, to
the nearest tenth of an hour, until there are 156 bacteria present?

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Linh Đan 4 years 2021-08-14T18:52:27+00:00 1 Answers 68 views 0

Answers ( )

  1. Nho
    0
    2021-08-14T18:53:39+00:00
    Reply

    Answer: 8.34 hr

    Step-by-step explanation:

    Given

    Initially, 100 bacteria are placed in a Petri dish

    bacteria doubles in every 13 hours

    So, a function that defines this relation is given as

    \Rightarrow B=B_o(2)^\frac{t}{13}

    where, B=\text{No of bacteria at any time}

    B_o=\text{Intial bacterias}\\t=\text{time in hrs}

    for B=156

    \Rightarrow 156=100\times 2^{\frac{t}{13}}\\\\\Rightarrow 1.56=2^{\frac{t}{13}}\\\\\Rightarrow t=13\times \dfrac{\ln (1.56)}{\ln (2)}\\\\\Rightarrow t=13\times0.641=8.34\ hr

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