Here are three functions of N. Assume that x^y means x raised to the yth power.
ID: 3556652 • Letter: H
Question
Here are three functions of N. Assume that x^y means x raised to the yth power.
(4*N) + 1
(N^4)
(4^N)
First, tell which of those three functions is considered polynomial.
If you let N be any non-negative integer, any one of these three functions could be larger. Give a value of N for which each of these functions is larger than the others. (Be sure to label your answers clearly.) That is, give a value for N that makes the first function bigger than the other two. Then give a value for N so that the second function bigger than the other two. Finally, give a value for N so that the third function is bigger than the other two.
As N becomes larger, one of the functions begins to grow more quickly than the other two; as N becomes larger and larger, which one of the three is going to be the biggest by far? (Note: feel free to use a spreadsheet or a small program to help you find the answer to this question.)
Explanation / Answer
-- The function ( (4*N) +1 ) is considered a polynomial.
-- Case 1 : Value of 'N' for '(4*N)+1' to be largest.
For N=1, (a) (4*N)+1 = 5. (b) (N^4) = 1. (c) (4^N) = 4.
Hence, answer is 1.
Case 2 : Value of 'N' for '(N^4)' to be largest.
For N=3, (a) (4*N)+1 = 13. (b) (N^4) = 81. (c) (4^N) = 64.
Hence, answer is 3.
Case 3 : Value of 'N' for '(4^N)' to be largest.
For N=10, (a) (4*N)+1 = 41. (b) (N^4) = 10000. (c) (4^N) = 1048576.
Hence, answer is 10.
-- As 'N' becomes larger and larger, the third function , (4^N), begins to grow more quickly than the other two. It'll we clear by substituting few values for 'N' in functions as shown below.
For N=5, (a) (4*N)+1 = 21. (b) (N^4) = 625. (c) (4^N) = 1024.
For N=10, (a) (4*N)+1 = 41. (b) (N^4) = 10000. (c) (4^N) = 1048576.
For N=15, (a) (4*N)+1 = 61. (b) (N^4) = 50625. (c) (4^N) = 1073741824.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.