For question (b), let’s analyze the pattern based on the Base Side Length and Total Number of Tiles:

1. Identify the pattern:

   • For each side length, the figure is a square grid. The total number of tiles is calculated by squaring the side length.

2. Fill in the values:

   • Base Side Length = 1 → Total Number of Tiles = $1^2 = 1$
   • Base Side Length = 2 → Total Number of Tiles = $2^2 = 4$
   • Base Side Length = 3 → Total Number of Tiles = $3^2 = 9$
   • Base Side Length = 4 → Total Number of Tiles = $4^2 = 16$

3. Determine if the relationship is linear or non-linear:

   • Since the relationship involves squaring the side length, this is a non-linear relationship (specifically quadratic).

4. Equation representing the relation:

   • The equation for the total number of tiles $T$ based on the base side length $n$ is: $T = n^2$

5. Extrapolate to the seventh step:

   • For a base side length of 7: $T = 7^2 = 49$

Thus, the table for part (b) is as follows:

The outcome for the seventh step would be 49 tiles.

Would you like further details or have any questions?

Related Questions:

1. How can you determine if a sequence is linear or non-linear based on first differences?
2. Can you describe other non-linear patterns similar to this quadratic relationship?
3. What would the graph of the equation $T = n^2$ look like?
4. How does the growth rate of a quadratic sequence compare to a linear sequence?
5. What are some real-life situations that follow a quadratic pattern like this one?

Tip: For non-linear relationships, especially quadratic ones, try plotting the points to see the curvature, which helps in visual identification.