Use an appropriate first-order differential equation to find the percentage of a given quantity of radium which remains after 100 years if we are told that the half-life of radium is 1600 years.

We know (example 1 on page 313 of Apostol) that radioactive decay is modeled by the first-order differential equation

All solutions to this equation are of the form . We are given that

Therefore,

Hence,

Therefore,

Thus, the percentage remaining after 100 years is