b. The area of another sheet of paper is 200 square inches. Write an equation that gives the area, $$ B $$, of this sheet of paper, in square inches, after being folded into thirds $$ n $$ times.

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To find the area $$ B $$ of a sheet of paper after being folded into thirds $$ n $$ times, we need to understand how folding affects the area.

1. **Initial Area**: The initial area of the sheet of paper is given as 200 square inches.

2. **Folding into Thirds**: When you fold a sheet of paper into thirds, the area is effectively reduced by a factor of $$ \frac{1}{3} $$ for each fold. This means that after one fold, the area becomes $$ \frac{1}{3} $$ of the original area.

3. **Generalizing for $$ n $$ Folds**: If the paper is folded $$ n $$ times, the area $$ B $$ can be expressed as:
   $$
   B = \text{Initial Area} \times \left(\frac{1}{3}\right)^n
   $$

4. **Substituting the Initial Area**: We substitute the initial area of 200 square inches into the equation:
   $$
   B = 200 \times \left(\frac{1}{3}\right)^n
   $$

Thus, the equation that gives the area $$ B $$ of the sheet of paper after being folded into thirds $$ n $$ times is:
$$
B = 200 \times \left(\frac{1}{3}\right)^n
$$
The area $$ B $$ after folding the paper $$ n $$ times is: $$ B = 200 \times \left(\frac{1}{3}\right)^n $$

b. The area of another sheet of paper is 200 square inches. Write an equation that gives the area, \( B \), of this sheet of paper, in square inches, after being folded into thirds \( n \) times.

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