Question

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

Answer 1

The equation that represents the relationship between step number and the number of dots is $y=5^n$.

Solution:

Let the number of dots be y.

Step number 0: Number of dots = 1

y = 1

Using exponential rule: $a^0=1$

$y=5^0$

Step number 1: Number of dots = 5

y = 5

$y=5^1$

Step number 2: Number of dots = 25

y = 25

$y=5^2$

Step number 3: Number of dots = 125

y = 125

$y=5^3$

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:

$y=5^n$

Number of dots = $5^n$.

Hence the equation that represents the relationship between step number and the number of dots is $y=5^n$.