10¹⁰⁰Years. Based on current understanding, the final stage in the history of a perpetually expanding universe would come about 10100 years from now. Such a large number is easy to write but difficult to understand. This problem investigates some of the incredible properties of very large numbers. a. The current age of the universe is around 10¹⁰ years. How much longer is a trillion years than this current age? How much longer is 10¹⁵ years? 10²⁰ years? b. Suppose protons decay with a half-life of 10³² years. When will the number of remaining protons be half its current amount? When will it be a quarter of its current amount? How many half-lives will have gone by when the universe reaches an age of 10³⁴ years? What fraction of the original protons will remain at this time? Is it reasonable to conclude that all protons in today’s universe will be gone by the time the universe is 10⁴⁰ years old? Explain.