Question

a piece of paper is folded in half. it is then folded in half again, and again...
x = the number of folds.
y = the thickness of the paper in inches.
images of graphs a, b, c, d showing thickness vs. number of folds

Explanation:

Step1: Analyze the relationship

When a paper is folded in half \( x \) times, the thickness \( y \) follows an exponential relationship. Let the initial thickness be \( t \). After \( x \) folds, the thickness \( y = t\times2^{x}\), which is an exponential function (not linear or other types shown in A, B, C).

Step2: Match with graphs

• Graph A: Has a flat and decreasing part, not exponential.
• Graph B: Linear, but our relationship is exponential.
• Graph C: Decreasing curve, opposite of what we need.
• Graph D: Shows an exponential growth curve (curving upwards, increasing rapidly), which matches \( y = t\times2^{x} \).

Answer:

D