which number is bigger?

- 2 to the power of n
- n to the power of 2020

Also, if we increase n gradually until infinity which of the two increase as the fastest time?

Reply 1

mqb2766

21

Original post by Carrying a torch

- 2 to the power of n
- n to the power of 2020

Also, if we increase n gradually until infinity which of the two increase as the fastest time?

Any ideas?

Im not sure your first question makes much sense (which is bigger) as it depends on n. You could take about n being "small" for the first part and "large" for the second part, which are obviously subjective.

However, the 2020 is a big number which you could change to plot. Try comparing 2^n with n^2 or n^3 or n^4. What happens, does the fact that the exponent is now 2020 really change anything?

If you;re comparing exponents, you could use a monotonic log() transformation.

(edited 2 years ago)

Reply 2

RogerOxon

21

Original post by Carrying a torch

- 2 to the power of n
- n to the power of 2020

Also, if we increase n gradually until infinity which of the two increase as the fastest time?

Try some values, e.g. 1, 2, 2020. Then look at the ratio of successive terms.

Reply 3

Carrying a torch

OP

9

Original post by mqb2766

Any ideas?

Im not sure your first question makes much sense (which is bigger) as it depends on n. You could take about n being "small" for the first part and "large" for the second part, which are obviously subjective.

However, the 2020 is a big number which you could change to plot. Try comparing 2^n with n^2 or n^3 or n^4. What happens, does the fact that the exponent is now 2020 really change anything?

If you;re comparing exponents, you could use a monotonic log() transformation.