Question

Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answer 1

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:

$1 \underset{+1}{\longrightarrow} 2 \underset{+3}{\longrightarrow} 5 \underset{+5}{\longrightarrow} 10$

Second differences:

$1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5$

Therefore, as the sequence of second difference is constant, the patten is quadratic.

The function for pattern B is:  $f(x)=x^2+1$

(where x is the step number)