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Math Help - Have I concluded a good formula

  1. #1
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    Have I concluded a good formula

    The population of animal in a country Park increases in number by 11 percent each year. A survey counted the number of animal in the park at the start of a particular year. If the number of animals counted was K, is the following formula connecting the current number, N, with time t in years since the initial count a correct formula to use?

    N = K x 11 x t
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  2. #2
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    Re: Have I concluded a good formula

    Quote Originally Posted by David Green View Post
    The population of animal in a country Park increases in number by 11 percent each year. A survey counted the number of animal in the park at the start of a particular year. If the number of animals counted was K, is the following formula connecting the current number, N, with time t in years since the initial count a correct formula to use?

    N = K x 11 x t
    1. Your formula is not correct.

    2. In the beginning, that means t = 0, you have K animals.

    After one year, t = 1, you have N(1)= K + K \cdot \underbrace{0.11}_{11\%} = K(1+0.11)

    Next year, t = 2, you have N(2)= K(1+0.11) + K (1+0.11)\cdot 0.11 = K(1+0.11)(1+0.11)=K(1+0.11)^2

    After x years, t = x, you have N(x)=K (1+0.11)^x
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  3. #3
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    Re: Have I concluded a good formula

    Quote Originally Posted by David Green View Post
    The population of animal in a country Park increases in number by 11 percent each year. A survey counted the number of animal in the park at the start of a particular year. If the number of animals counted was K, is the following formula connecting the current number, N, with time t in years since the initial count a correct formula to use?
    N = K x 11 x t
    At the start N_0=K.
    Then after one year N_1=N_0+0.11N_0=1.11K
    After two years N_2=N_1+0.11N_1+=(1.11)^2K
    So after t years N_t=~?
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  4. #4
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    Re: Have I concluded a good formula

    Quote Originally Posted by earboth View Post
    1. Your formula is not correct.

    2. In the beginning, that means t = 0, you have K animals.

    After one year, t = 1, you have N(1)= K + K \cdot \underbrace{0.11}_{11\%} = K(1+0.11)

    Next year, t = 2, you have N(2)= K(1+0.11) + K (1+0.11)\cdot 0.11 = K(1+0.11)(1+0.11)=K(1+0.11)^2

    After x years, t = x, you have N(x)=K (1+0.11)^x
    Thanks for your help, I read it as; N(x) = K x 1.11^x
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