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:

Option 2) 5ⁿ < n⁵

To determine the asymptotic order of growth, we compare the growth rates of the two terms in the function. In this case, the exponential term 5ⁿ grows faster than the polynomial term n⁵ as n approaches infinity. Therefore, we can conclude that 5ⁿ is less than n⁵.