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 26?

Answer 1

The computer algorithm executes twice as many operations when the input size increases by 1. By using this information and calculating the operations for each input size, we find that it executes 26,624 operations for an input size of 26.

Step-by-step explanation:

To find out how many operations the computer algorithm executes when it is run with an input of size 26, we can use the given information. The algorithm executes twice as many operations when the input size increases by 1. So, if it executes 7 operations for an input size of 1, it would execute 14 operations for an input size of 2, 28 operations for an input size of 3, and so on.

Since the algorithm executes twice as many operations for each increase in input size, we can see that it follows a pattern of doubling. We can calculate the number of operations for an input size of 26 by doubling the number of operations for an input size of 25. Continuing this calculation, we get:

Input Size 1: 7 operations
Input Size 2: 14 operations
Input Size 3: 28 operations
...

Input Size 25: 13,312 operations
Input Size 26: 26,624 operations