1. Tyler has a piece of paper and is sharing it with Elena, Clare, and Andre. He cuts the paper to create 4 equal pieces, then hands 1 piece each to the others and keeps 1 for himself. What fraction of the original piece of paper does each person have?
2. Tyler then takes his remaining paper and does it again. He cuts the paper to create 4 equal pieces, then hands 1 piece each to the others and keeps 1 for himself. What fraction of the original piece of paper does each person have now?
3. Tyler then takes his remaining paper and does it again. What fraction of the original piece of paper does each person have now? What happens after more steps of the same process?

Here is a geometric shape built in steps.

• Step 0 is an equilateral triangle.

• To go from Step 0 to Step 1, take every edge of Step 0 and replace its middle third with an outward-facing equilateral triangle.

• To go from Step 1 to Step 2, take every edge of Step 1 and replace its middle third with an outward-facing equilateral triangle.

• This process can continue to create any step of the design.

1. Find an equation to represent function , where is the number of sides in Step . What is ?
2. Consider a different function , where is the number of new triangles added when drawing Step . Let  How many new triangles are there in Steps 1, 2, and 3? Explain how you know.
3. What is the total number of triangles used in building Step 3?