We fold the paper ​n​ times, so its thickness becomes

Since ​0.1mm=10−7km,

We need ​tn​≥384000km. By guessing:

We see ​10​ folds is far too few. So we try:

Clearly, we overadjusted, as ​100​ would be far too many folds. Now that we know Jimmy should make between ​10​ and ​100​ folds we make successive guesses:

At ​n=40, ​t40​≈110000​ km, still about a third of Jimmy's desired thickness of ​384000​ km. One more fold doubles it, which would not be enough, but two more folds will quadruple the thickness to about ​440000km:

which exceeds ​384 000​ km. Hence Jimmy must fold the paper ​42​ times.

As you can see, we do not yet have a good way to solve problems in which we need solve exponentials with very large powers. In this lesson, we will learn a more systemic way to solve problems like Jimmy's.

We fold the paper ​n​ times, so its thickness becomes

Since ​0.1mm=10−7km,

We need ​tn​≥384000km. By guessing:

We see ​10​ folds is far too few. So we try:

Clearly, we overadjusted, as ​100​ would be far too many folds. Now that we know Jimmy should make between ​10​ and ​100​ folds we make successive guesses:

At ​n=40, ​t40​≈110000​ km, still about a third of Jimmy's desired thickness of ​384000​ km. One more fold doubles it, which would not be enough, but two more folds will quadruple the thickness to about ​440000km:

which exceeds ​384 000​ km. Hence Jimmy must fold the paper ​42​ times.

As you can see, we do not yet have a good way to solve problems in which we need solve exponentials with very large powers. In this lesson, we will learn a more systemic way to solve problems like Jimmy's.