5. Arrange the functionsn , 1000 log n, n log n, 2n!, 2n, 3n, and n2/1,000,000 in a list sothat each function is big-O of the next function.

The functions arranged in ascending order of growth rates (each function is big-O of the next function) are:

1. n
2. 1000 log n
3. n log n
4. n^2/1,000,000
5. 2^n
6. 3^n
7. 2n!

Explanation:

1. n: This is a linear function and has the lowest growth rate among all the given functions.

2. 1000 log n: Logarithmic functions grow slower than linear functions for large n.

3. n log n: This is a linearithmic function and grows faster than both linear and logarithmic functions.

4. n^2/1,000,000: This is a quadratic function. Despite the large denominator, for sufficiently large n, this function will eventually outgrow the previous ones.

5. 2^n: This is an exponential function, which grows faster than polynomial functions like n^2.

6. 3^n: This is also an exponential function, but with a larger base than 2^n, so it grows faster.

7. 2n!: This is a factorial function, which grows faster than exponential functions.