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22 April, 21:43

Conservationists tagged 120 black-nosed rabbits in a national forest in 1990. In 1991 , they tagged 240 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 9 years from 1990?

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  1. 22 April, 21:48
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    Hence after period of 9 years from 1990 t0 1999 will be 61438 rabbits.

    Step-by-step explanation:

    Given:

    Population for rabbit obeys exponential law.

    120 at 1990 and 240 1991 ... after 1 year time period

    To Find:

    After 9 year time period how many rabbits will be there.

    Solution:

    Exponential law goes on present value and various value and time period and defined as,

    let Y be present value Y0 previous year value and k exponential constant and t be time period.

    So

    Y=Y0e^ (kt)

    Here Y=240, Y0=120 t=1 year time period

    So

    240=120e^ (k*1)

    240/120=e^k

    2=e^k

    Now taking log on both side, [natural log]

    ln (2) = ln (e^k)

    ln (2) = kln (e)

    k=ln (2)

    k=0.6931

    For t=9 year of time period

    Y0=120, t=9, k=0.6931

    Y=Y0e^ (k*t)

    Y=120*e^ (0.6931*9)

    =120e^6.2383

    =61438.48

    =61438 rabbits
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