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1 vote
Rank the following functions by increasing order of growth:

1. log( n! )
2. 10000n²
3. log(n³)
4. 2ⁿ
5. n²log(n)

1 Answer

3 votes

Final answer:

The functions ranked by increasing order of growth are log(n!), n²log(n), log(n³), 10000n², and 2ⁿ.

Step-by-step explanation:

  1. Rank the functions by increasing order of growth:
  2. log( n! ) - This function has a logarithmic growth rate, which means the growth rate of the function decreases as n increases. Therefore, it has the slowest growth rate among the given functions.
  3. n²log(n) - This function has a quadratic growth rate, which means the growth rate of the function increases as n increases. Therefore, it has a faster growth rate than log(n!).
  4. log(n³) - This function has a growth rate between logarithmic and quadratic. It increases slower than n²log(n) but faster than log(n!).
  5. 10000n² - This function has a quadratic growth rate, which means the growth rate of the function increases at a faster pace compared to log(n³).
  6. 2ⁿ - This function has an exponential growth rate, which means the growth rate of the function increases significantly as n increases. Therefore, it has the fastest growth rate among the given functions.

User Andy Macleod
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