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Question
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 – 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 22? For each integer n 2 1, let s, be the number of operations the algorithm executes when it is run with an input of size n. Then 1 7.2k for each integer k > 1. Therefore, So, S1, S21 So and is a geometric sequence with = 17 Sk constant multiplier which is 2 . So, for every integer n 2 0, s, 7.2* . It follows that for an input of size 22, the number of operations executed by the algorithm is s which equals 58720256 22
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Transcribed Image Text: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 – 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 22? For each integer n 2 1, let s, be the number of operations the algorithm executes when it is run with an input of size n. Then 1 7.2k for each integer k > 1. Therefore, So, S1, S21 So and is a geometric sequence with = 17 Sk constant multiplier which is 2 . So, for every integer n 2 0, s, 7.2* . It follows that for an input of size 22, the number of operations executed by the algorithm is s which equals 58720256 22
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