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    1)prove that

    tanx + cot x = 2cosec(2x)

    2) a population of deer is introduced into a park. the population 'p' at time 't' years after the deer have been introduced is modelled by :

    P = 2000a^t / 4 + a^t

    'a' is a constant. given that there are 800 deer in the park after 6 years, and 'a' is 1.1776,

    use the model to predict the number of years needed for the population of deer to increase from 800 to 1800.

    Thanks
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    1) LHS = sinx/cosx + cosx/sinx
    = (sin^2x + cos^2x)/sinxcosx
    =2/sin2x
    = RHS
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    2) This is pretty straight forward.....

    1800 = 2000a^t / 4 + a^t
    1800(4+a^t) = 2000a^t
    7200 + 1800a^t = 2000a^t
    7200 = 200a^t

    36 = a^t

    Now you need to take logs here to get t

    ln 36 = ln a^t
    ln 36 = t ln a (logs rule)

    t = ln 36 / ln a

    Insert the value of A to find T
    t = 21.9 or 22 years

    Your given that it took 6 years to get a population of 800
    so the difference = 22 - 6

    answer = 16 years
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    (Original post by xskater)
    2) This is pretty straight forward.....

    1800 = 2000a^t / 4 + a^t
    1800(4+a^t) = 2000a^t
    7200 + 1800a^t = 2000a^t
    7200 = 200a^t

    36 = a^t

    Now you need to take logs here to get t

    ln 36 = ln a^t
    ln 36 = t ln a (logs rule)

    t = ln 36 / ln a

    Insert the value of A to find T
    t = 21.9 or 22 years

    Your given that it took 6 years to get a population of 800
    so the difference = 22 - 6

    answer = 16 years
    ahhh. thank u
 
 
 
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