OpenStax College Physics for AP® Courses, Chapter 1, Problem 30 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. We are going to estimate the number of generations that have passed since the year 0 AD. Now the current year is 2019 so that means the numbers of years that have passed is 2019 minus 0 or 2019 years. Now we have to make an estimate of how many years are in a lifetime and I'm gonna guess it's about 60 years and we are multiplying also by one generation for every one-third of a lifetime and I knew to set up the fraction's this way because we want to know the number of generations and so we need a fraction that has generations; you can think of that as a unit in the top of the fraction and so I know there's one generation for every one-third of a lifetime— this is what the question tells us— and so that means we need the next fraction to have lifetime on the top so that it cancels with this lifetime unit and divide it by years because we are going to be multiplying by years here. And so one lifetime for every 60 years which is a guess and I'm probably guessing too high because lifetime's in the past were much shorter and so we should be using a number here that's sort of an average over all those years but I don't really know what that average should be, let's just say 60 for the sake of guessing, and then we multiply by the number of years. So this works out to 100.95 generations and this chapter 1 is all about significant figures and so on so we should, you know, write this in a way that reflects what precision is appropriate for the question and there's a lot of guessing going on so we can't be that precise and let's suppose this has two significant figures here in which case our answer will have two significant figures. So 1.0 times 10 to the 2 generations have passed.