1. ## 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

2. Originally Posted by centenial
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

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

then use these with some arguments to order your set.

Originally Posted by centenial

f. 2^200
This does not grow at all.

3. Another helpful tip: the order of a function $\displaystyle f(x)$ which is a sum of functions $\displaystyle g_i(x)$ is the same as the order of the function $\displaystyle g_{max}(x)$ with the highest order of the $\displaystyle g_i(x)$.