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
.
Answer:3x^2-5x+2=0
Step-by-step explanation:
Format of a quadratic equation= ax^2 +bx+c
Let x=1 and 2/3
When x=1
x-1=0.......(1)
When x=2/3
x-2/3=0.........(2)
Compare the equations
(x-1)(x-2/3)=0
x^2-2/3x-x+2/3=0
x^2-5/3x+2/3=0
Multiply all terms by 3
3x^2-5x+2=0
2 * ( x - 15 ) = 1.5 * x
2x - 30 = 1.5x
2x -1.5x = 30
0.5x = 30
x = 30/0.5
x = 60mph.