Exponential growth with folding: 1 mm thick paper doubles in thickness each fold If a sheet of paper is 1 mm thick and thickness doubles with every fold, what is the approximate thickness after 50 folds (expressed in kilometres)?

Introduction / Context:This problem highlights exponential growth: each fold doubles thickness. After many folds, values explode in size, demonstrating how powers of 2 scale. The twist is expressing millimetres in kilometres.

Given Data / Assumptions:

• Initial thickness t0 = 1 mm.
• Each fold doubles thickness: after n folds, thickness tn = t0 * 2^n.
• We need t50 in kilometres. Unit relation: 1 km = 10^6 mm.

Concept / Approach:Compute 2^50 and convert millimetres to kilometres. Use approximate values for powers of two to match the nearest option.

Step-by-Step Solution:

Verification / Alternative check:Another route: 2^50 ≈ 1.1259 * 10^15; dividing by 10^6 gives ≈ 1.1259 * 10^9 km. This corroborates the “about 1 billion km” choice.

Why Other Options Are Wrong:

• 100 km, 1000 km: Far too small; exponential doubling produces astronomically large values.
• 1 million km: Still three orders of magnitude too small compared with about 1.1 billion km.

Common Pitfalls:Confusing “area halved” with thickness behavior—folding halves area but doubles thickness; also mixing up unit conversions between mm and km.

Final Answer:1 billion km