A grey squirrel population was introduced in a certain county of Great Britain 30 years ago. Biologists observe that the population doubles

Question

A grey squirrel population was introduced in a certain county of Great Britain 30 years ago. Biologists observe that the population doubles every 6 years, and now the population is 100,000. what is the formula

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Calantha 4 years 2021-08-16T09:50:30+00:00 1 Answers 40 views 0

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  1. Bo
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    2021-08-16T09:51:40+00:00
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    Answer:

    The formula for the gray squirrel population is n = 3125\cdot 2^{\frac{t}{6} }.

    Step-by-step explanation:

    The statement indicates that gray squirrel population increases geometrically, population is doubled every 6 years. That is:

    \frac{n_{t+6}}{n_{t}} = 2 (1)

    If the population after 30 years is 100000, then we construct the following relationship:

    \frac{n_{6}}{n_{o}} \cdot \frac{n_{12}}{n_{6}}\cdot \frac{n_{18}}{n_{12}}\cdot \frac{n_{24}}{n_{18}}\cdot \frac{n_{30}}{n_{24}} = 2^{5}

    n_{30} = 2^{5}\cdot n_{o}

    n_{o} = \frac{n_{30}}{2^{5}} (2)

    n_{o} = \frac{100000}{2^{5}}

    n_{o} = 3125

    A geometric progression for the grey squirrel population is defined by the following formula:

    n = 3125\cdot 2^{\frac{t}{6} } (3)

    Where:

    t – Time, measured in years.

    n – Population of gray squirrels.

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