Hank is studying a population of bacteria and notices that the bacteria population decreases by 5% each hour. The function that represents

Question

Hank is studying a population of bacteria and notices that the bacteria population decreases by 5% each hour. The function that represents the population of bacteria has a constant percent rate of change.

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Vivian 3 weeks 2021-11-08T22:37:10+00:00 1 Answer 0 views 0

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    2021-11-08T22:38:52+00:00

    Answer: Pupulation = A*0.95^t

    where t is the numer of hours that has passed, and A is the initial population of the bacteria.

    Step-by-step explanation:

    If the initial population of bacteria is A.

    After one hour we can see that the population has decreaesed by 5%, so the new population is

    P = A – 0.5*A = 0.95*A

    After other our, the population decreased by 5% again, the new population is:

    P = (0.95*A) – 0.5*(0.95*A) = 0.95*0.95*A = A*0.95^2

    And so on.

    This is an exponential decay, so we can write this relation as:

    Pupulation = A*0.95^t

    where t is the numer of hours that has passed, and A is the initial population of the bacteria.

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