# Rule of 70 Exercise

A Platonic change of y% always corresponds to multiplying by exp(.01 y). Approximating ln(2) as if it were exactly .7, this means that a 70% Platonic change corresponds to multiplying by 2. A -70% Platonic change corresponds to multiplying by .5. A 140% Platonic change corresponds to multiplying by 4. In this exercise, you are asked to mark which range the multiplication factor is in for the Platonic percentage changes shown at the top. Please act as if ln(2) were exactly equal to .7 so that a 70% Platonic change is exactly a doubling.

Notice that a 70% Platonic change is multiplying by 2, which in turn is a 100% Earthly percentage change. A -70% Platonic change is multiplying by .5, which is a -50% Earthly percentage change. One illustration of how Platonic changes can be more convenient that Earthly percentage changes is that a 70% Platonic change followed by a -70% Platonic change gets you back to where you started. But a 100% Earthly percentage change followed by a -100% Earthly percentage change gets you to zero. And a 50% Earthly percentage change followed by a -50% Earthly percentage change gets you a -25% overall Earthly percentage change.

If you want the exercise as a pdf with the questions on one side and the answers on the other, here it is. Or here it is on this blog post:

Answers are below.