Write an equation to represent the relationship between the step number, n, and the number of dots, y.

The equation that represents the relationship between step number and the number of dots is .

Solution:

Let the number of dots be y.

Step number 0: Number of dots = 1

y = 1

Using exponential rule:

Step number 1: Number of dots = 5

y = 5

Step number 2: Number of dots = 25

y = 25

Step number 3: Number of dots = 125

y = 125

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:

Number of dots = .

Hence the equation that represents the relationship between step number and the number of dots is .

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