What is the order of each of the following growth functions?a. 10n2 + 100n + 1000b. 10n3 - 7c. 2n + 100n3d. n2 log n
Question
What is the order of each of the following growth functions?a. 10n2 + 100n + 1000b. 10n3 - 7c. 2n + 100n3d. n2 log n
Solution
a. The order of the function 10n^2 + 100n + 1000 is O(n^2). This is because when determining the order of a function, we look at the term with the highest degree, which in this case is n^2.
b. The order of the function 10n^3 - 7 is O(n^3). Again, we look at the term with the highest degree, which is n^3.
c. The order of the function 2n + 100n^3 is O(n^3). Despite the presence of a term in n, the n^3 term dominates for large n, so the order is determined by the n^3 term.
d. The order of the function n^2 log n is O(n^2 log n). This is a bit different from the previous examples because it involves a logarithm, but the principle is the same: the term with the highest degree (in this case, n^2 log n) determines the order.
Similar Questions
Consider the following functions.f1(n) = (log n)2023f2(n) = n2logn(nn)f3(n) = n3+ 7n2f4(n) = 2. 023nf5(n) = n log nf6(n) = n *3n2Now do the followings:a. Write a correct asymptotic upper bound for each of the above.b. Sort the functions in ascending order of their growth rate, assuming n is significantlylarge. Just write the sorted order, no need to show any simulation.
For each of the following pairs of functions, indicate whether the first functionof each of the following pairs has a lower, same, or higher order of growth (towithin a constant multiple) than the second function.a. n(n + 1) and 2000n2 b. 100n2 and 0.01n3c. log 2 n and ln n d. log 22 n and log 2 n2e. 2n−1 and 2n f. (n − 1)! and n!
Which of the following is the correct order of growth from fastest to slowest?O(1), O(n), O(n log n), O(n^2)O(n^2), O(n log n), O(n), O(1)O(n log n), O(n), O(1), O(n^2)O(n), O(1), O(n^2), O(n log n)
Please rank the following functions by their rate of growth and prove your answer.
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
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.