For what natural n>1 does the inequality 2^n>=n^3

Answer 1

Try graphing each of these functions to see where the graph for 2^n >= the graph for n^3. Then remember that the question is limiting n to natural numbers > 1, i.e., n must be a counting number 2, 3, 4, ...

You may also make a table of values:

n: 2^n n^3

2 4 8

3 8 27

4 16 64

5 32 125

6 64 216

7 128 343

8 256 412 Continue until 2^n >= n^3

9