Answer:
[tex]y = 2^x - 1[/tex]
Step-by-step explanation:
Let the number of disks be x and the minimum number of moves be y.
[tex]y = 2^x - 1[/tex]
When x = 1: y = 1
[tex]y = 1 = 2 - 1 = 2^1 - 1[/tex]
When x = 2: y = 3
[tex]y = 3 = 4 - 1 = 2^2 - 1[/tex]
When x = 3: y = 7
[tex]y = 7 = 8 - 1 = 2^3 - 1[/tex]
When x=4: y = 15
[tex]y = 15 = 16 - 1 = 2^4 - 1[/tex]
When x = 5: y = 31
[tex]y = 31 = 32 - 1 = 2^5 - 1[/tex]
Notice that for each derived expression of y, the exponent of 2 is being replaced by the value of x.
The general equation is: [tex]y = 2^x - 1[/tex]
