MATH SOLVE

3 months ago

Q:
# A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k β 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 24?

Accepted Solution

A:

Using a geometric sequence, it is found that it executes 117,440,512 operations when it is run with an input of size 24.What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.The nth term of a geometric sequence is given by:[tex]a_n = a_1q^{n-1}[/tex]In which [tex]a_1[/tex] is the first term.In this problem:Since the algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k β 1, the common ratio is q = 2.When the algorithm is run with an input of size 1, it executes seven operations, hence the first term is [tex]a_1 = 7[/tex].Then, for a input size of n, the number of operations is given by:[tex]a_N = 7(2)^n[/tex]Then, for a input size of 24:[tex]a_{24} = 7 \times 2^{24} = 117440512[/tex]It executes 117,440,512 operations when it is run with an input of size 24.More can be learned about geometric sequences at