There is a branch of mathematics that covers populations. We all know the name of this branch of maths: demographics.
There are two types of populations studied by demographics: general and static. General is like a population of plants or critters—they are born/seeds germinated, grow, reproduce and finally die. General demographics.
The other type of population is fixed, a population of tyres made in a month, a population of glass figurines.
The first type of population can swell, decline, even die out—seen any non–avian dinosaurs lately? The second—a set of glass figurines—once created can only decrease as members of the population are broken. Any use in studying this type of demographic. Well, HELL YEAH!
You are a tyre manufacturer. You need to offer a warranty period to cover buyers against manufacturer’s error—a new tyre shouldn’t blow out with only 5K of travel! You don’t want to be too generous else harder wearing uses than normal start getting tyres replaced for free.
So the manufacturer employs a demographer who studies the population of tyres made in a month. Say he finds that after 51,000Km tyres start wearing out. So the manufacturer offers a warranty for 50,000Km. Nice and generous looking, safely under the age tyres start wearing out.
Demographic data comes in a table showing the population size at various ages, the table sort of looks like a table of logarithms—you need to extract the useful data from that. There are uncertainties in the data—some idiots drive with tyres overinflated, some have tyres under-inflated. Some drive on smooth asphalt in cities, others spend their time driving a high speed over asphalt on highways/freeways, others drive mainly on dirt roads.
Whatever—you need to come up with a figure where the warranty should cut out.
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