Answer:
1. In order for Pattern B to be linear, the common difference of the number of dots between each step should be constant. As it is not constant, the pattern is not linear.
2. In order for Pattern B to be exponential, the common ratio of the number of dots between each step should be constant. As it is not constant, the pattern is not exponential.
3. In order for Pattern B to be quadratic, its sequence of second differences must be constant.
First differences:
[tex]1 \underset{+1}{\longrightarrow} 2 \underset{+3}{\longrightarrow} 5 \underset{+5}{\longrightarrow} 10[/tex]
Second differences:
[tex]1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5[/tex]
Therefore, as the sequence of second difference is constant, the patten is quadratic.
The function for pattern B is: [tex]f(x)=x^2+1[/tex]
(where x is the step number)
