Regents Exam: Algebra I August 2016 (Problem 27 of 37)

The video tutorial discusses a pattern of squares and explores whether a linear or exponential model best predicts the number of squares in subsequent iterations. The pattern starts with 2 squares, then 4, and finally 8 in the third iteration. By analyzing the differences between iterations, it is determined that a linear model is unsuitable as the increase is not constant. Instead, the pattern follows an exponential model, specifically 2 raised to the power of N, where N is a positive integer. This model accurately predicts the number of squares in each iteration, confirming the exponential nature of the pattern.

What is the main task in determining the pattern of squares?

• Counting the number of squares in the first iteration

• Identifying the color of the squares

• Determining the type of model to predict the pattern

• Finding the area of each square

Why is a linear model not suitable for this pattern?

• The pattern decreases over time

• The pattern increases at a constant rate

• The pattern does not increase at a constant rate

• The pattern is unpredictable

How many squares are there in the third iteration of the pattern?

• 4 squares

• 10 squares

• 6 squares

• 8 squares

What is the formula used to describe the exponential model in this pattern?

• 2 times N

• 2 raised to the power of N

• N squared

• N plus 2

What does N represent in the exponential model 2^N?

• A decimal number

• A positive integer greater than zero

• A negative integer

• A fraction