List the following functions according to their order of growth from the lowestto the highest:(n2 + 3)!, 2 lg(n + 50)5, 33n , 0.05n10 + 3n3 + 1, ln 3 n, √n, 32n

The functions listed in order of growth from lowest to highest are:

√n, ln 3n, 2 lg(n + 50)5, 0.05n10 + 3n3 + 1, 33n, 32n, (n2 + 3)!

Here's why:

1. √n: This is a square root function, which grows slower than linear, logarithmic, polynomial, and exponential functions.

2. ln 3n: This is a logarithmic function, which grows slower than polynomial and exponential functions, but faster than the square root function.

3. 2 lg(n + 50)5: This is a logarithmic function, which grows slower than polynomial and exponential functions, but faster than the square root function. It grows faster than ln 3n because of the larger base and exponent.

4. 0.05n10 + 3n3 + 1: This is a polynomial function, which grows slower than exponential functions, but faster than logarithmic and square root functions. The dominant term here is 0.05n10.

5. 33n: This is an exponential function, which grows faster than polynomial, logarithmic, and square root functions, but slower than the factorial function.

6. 32n: This is also an exponential function, which grows faster than 33n because of the larger base.

7. (n2 + 3)!: This is a factorial function, which grows faster than all other types of functions listed here.