Chris is a researcher at the Centers for Disease Control and Prevention, and he is trying to understand the behavior of a new and dang

Question

Chris is a researcher at the Centers for Disease Control and Prevention, and he is trying to understand the behavior of a new
and dangerous virus. He starts his experiment with 25 viruses that grow at a rate of 75% per hour. He will check on the
viruses in 12 hours. How many viruses will he find? Round your answer to the nearest whole number.

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Everleigh 15 mins 2021-09-15T02:11:34+00:00 2 Answers 0

Answers ( )

    0
    2021-09-15T02:12:40+00:00

    Answer:202,577 viruses

    0
    2021-09-15T02:13:06+00:00

    Answer:

    Chris  will find 20625 viruses in 12 hours

    Step-by-step explanation:

    Geometric Progressions

    The geometric progression can be understood as a sequence or ordered terms when the term n equals the previous term n-1 by a constant value called the common ratio

    a_n=a_{n-1}r

    Recursively going back we find that

    a_n=a_1r^n

    Being a_1 the first term of the sequence

    Chris’ experiment shows that viruses grow at a rate of 75% per hour. It means that we get the next generation of viruses as the previous by 1.75. This is the common ratio. We also know he starts his experiment with 25 viruses, this makes

    a_1=25\ ,\ r=1.75

    We can now express the number of viruses as a function of the number of hours n:

    a_n=25\left ( 1.75 \right )^n

    We are required to compute the number of viruses found when n=12 hours:

    a_{12}=25\left ( 1.75 \right )^{12}

    a_{12}=25(825)

    a_{12}=20625 \ viruses

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