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13 January, 16:00

The population of a colony of mosquitoes grows exponentially according to the function P (t) = P0ekt.

a) If there are 1,000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days?

b) How long will it take the colony to reach 10,000 mosquitoes?

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  1. 13 January, 17:17
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    The answer to your question is:

    a) P (3) = 5818 mosquitoes

    b) 4 days

    Step-by-step explanation:

    Data

    P (t) = Poekt

    a)

    Po = 1000 mosquitoes

    Pt = 1800

    t = 1 day

    P (3) = ?

    1800 = 1000 e1k

    1800 / 1000 = e 1k

    e 1k = 1.8

    1k = In 1.8

    k = 0.587

    P (3) = 1000 e (0.587) (3)

    P (3) = 1000 e 1.761

    P (3) = 5818. 2 mosquitoes

    b)

    P (t) = 10,000

    10000 = 1000 e 0.587t

    10000 / 1000 = e 0.587t

    10 = e 0.587t

    In 10 = in e 0.587t

    2.3 = 0.587t

    t = 3.92 days ≈ 4 days
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