To determine the number of times a piece of paper must be folded to exceed a certain thickness, we can use the concept of exponential growth.
Each time the paper is folded in half, the thickness doubles. So, if we start with a thickness of 0.1 mm and fold it once, it becomes 0.2 mm thick. Folding it again doubles that thickness to 0.4 mm, and so on.
We can express the thickness of the folded paper after n folds as:
Thickness = 0.1 mm * 2^n
We want the thickness to be greater than 0.5 mm, or 1/2 mm. So we can set up the following inequality:
0.1 mm * 2^n > 0.5 mm
Simplifying the inequality:
2^n > 5
Now, let's solve for n by taking the logarithm of both sides:
log2(2^n) > log2(5)
n > log2(5)
Using a calculator or rounding to the nearest whole number, we find that log2(5) is approximately 2.322.
Therefore, the paper must be folded at least 3 times (n > 2.322) for the folded paper to be more substantial than 1/2 mm thick.