Question

Select the correct inequality for the asymptotic order of growth of the function 5ⁿ - n⁵?

1) 5ⁿ > n⁵
2) 5ⁿ < n⁵
3) 5ⁿ = n⁵
4) Cannot be determined

Answer 1

The correct inequality for the asymptotic order of growth of the function 5ⁿ - n⁵ is 5ⁿ > n⁵.

Step-by-step explanation:

The correct inequality for the asymptotic order of growth of the function 5ⁿ - n⁵ is 5ⁿ > n⁵.

To understand why this is the correct inequality, we can look at the behavior of the terms as n becomes very large. The term 5ⁿ grows exponentially, as the base (5) is greater than 1. On the other hand, the term n⁵ grows polynomially, as the exponent (5) is larger than 1. Therefore, as n becomes very large, 5ⁿ will eventually be greater than n⁵, resulting in the inequality 5ⁿ > n⁵.