The equation that represents the relationship between step number and the number of dots is [tex]y=5^n[/tex].
Solution:
Let the number of dots be y.
Step number 0: Number of dots = 1
y = 1
Using exponential rule: [tex]a^0=1[/tex]
[tex]y=5^0[/tex]
Step number 1: Number of dots = 5
y = 5
[tex]y=5^1[/tex]
Step number 2: Number of dots = 25
y = 25
[tex]y=5^2[/tex]
Step number 3: Number of dots = 125
y = 125
[tex]y=5^3[/tex]
Note that in step number 0 the power is 0, 1st step power of 5 is 1, 2nd step power of 5 is 2 and the third step power of 5 is 3.
If the process goes on up to n steps, then power of 5 is n.
∴ Step number n:
[tex]y=5^n[/tex]
Number of dots = [tex]5^n[/tex].
Hence the equation that represents the relationship between step number and the number of dots is [tex]y=5^n[/tex].
