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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, - 1 be the number of operations the algorithm executes when it is run with an input of size n. Then 7 and s =7.2k for each integer k 2 1. Therefore, so, S1, S2, ... is a geometric sequence So = with 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 s22 which equals 58720256

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, - 1 be the number of operations the algorithm executes when it is run with an input of size n. Then 7 and s =7.2k for each integer k 2 1. Therefore, so, S1, S2, ... is a geometric sequence So = with 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 s22 which equals 58720256

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 52E
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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
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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