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Math Help - function growth rate

  1. #1
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    function growth rate

    I'm not sure about the best way to approach this problem. Are there specific steps to solve or know this, other than simply plugging numbers into the functions?

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    Order the following functions by growth rate:

    a. 4*n*log(n) + sqrt(n)
    b. 2^(log(n^2))
    c. 3*n + 20 log n^2
    d. n^3
    e. n*log(n)
    f. 2^200
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  2. #2
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    Quote Originally Posted by centenial View Post
    I'm not sure about the best way to approach this problem. Are there specific steps to solve or know this, other than simply plugging numbers into the functions?
    You need to know the order of each simple function i.e

    \ln(n) < n< n^2 <n^3< \dots < 2^n <3^n < \dots< n!


    then use these with some arguments to order your set.


    Quote Originally Posted by centenial View Post

    f. 2^200
    This does not grow at all.
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  3. #3
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    Another helpful tip: the order of a function f(x) which is a sum of functions g_i(x) is the same as the order of the function g_{max}(x) with the highest order of the g_i(x).
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