Please solve and answer

Problem 3: Paper-Folding Patterns Take a piece of paper, and fold it in half as many times as you can. After I fold, there will be 2 regions. How many regions will occur after 3 folds? Four folds? How many folds are possible? Complete the table below. Imagine that there is no limit to the number of folds possible. # of folds 0 # of Regions 2 Questions 1. Describe patterns found in the table. 3. 4 5 10 100 N 16 32 1024 N.2 2. Describe how the number of regions is related to the number of folds. Translate this relationship into an algebraic rule. Use this rule to determine the number of regions given 18 folds. 3. Add another heading to the table: Area of the smallest region. Complete the table under this heading. 4. Describe patterns observed in the table. How is the area related to the number of folds? Describe the relationship algebraically. 5. Graph both relationships. How are they alike? Different?