Part two: how to recognise exponential growthĪ simple way to look out for exponential growth is to try to spot a doubling time. Reported cases of covid-19 in the UK in the month before lockdown measures were announced. Decide for yourself: is the number of cases roughly doubling between each highlighted row? The “exponential growth” way of looking at this data is not exactly right, but in my view it’s not far wrong.Īs we have written previously, the date column can’t be taken too literally: this is the date of reporting, but not the date a case happened. From that 22%, I calculate a doubling time of 2.7 days, so I’ve highlighted in bold, every third day in the table. Our second way of understanding exponential growth is to think of doubling times. That’s our first concept of exponential growth. On average, it’s about 22% of the number of existing cases. The number of new cases goes up with the number of existing cases. (At this time, there was no community testing: this is the number of hospitalised confirmed cases of covid-19.) We notice immediately that there is not a fixed rate of growth: it’s not 10 new cases per day, or 50 cases per day, or a thousand cases per day. The Table shows the number of confirmed covid-19 cases in the UK in 2020 before the run up to the “lockdown” on 23 rd March (source:, accessed ). We will see that this can, and did, apply to epidemics such as the covid-19 pandemic. A founding principle of medical statistics is that “all models are wrong, but some models are useful” ( attributed to GEP Box ).īy ‘model’ we mean a mathematical model, and by a mathematical model we mean the idea that a mathematical formulation can match something that happens in the real world. Nevertheless, it is often a good match for things that happen in the real world. In the real world, exponential growth can’t carry on indefinitely. Of course, you’ve noticed that we’re glossing over some inconvenient details, such as mortality, that will dent the growth of the numbers of red kites. The population the year after will be twice as big again, and so on. Then the population next year (in our hypothetical, infinitely resourced and hazard-free environment for red kites) will be twice as big as the population next year. Suppose (for the sake of argument) each year a typical pair of red kites have two young who successfully reach breeding age. When there’s a fixed doubling time, we have exponential growth. Here’s another way to understand exponential growth, equally correct. Whatever the increase is this year, next year there will be more red kites – and the increase will be greater than this year. We can’t say that the increase is 10 red kites per year, or 20 red kites per year, or any fixed number of red kites per year. Notice that there is not a single speed of growth. The rate of growth is proportional to the current number of red kites. If there are 20 red kites in the breeding population, they will have twice as many chicks as if there are 10 red kites in the breeding population. A textbook example is to imagine a small population of red kites living in a large, food-rich, predator-free countryside. Here’s how I learnt exponential growth in maths class: when the speed of growth is proportional to the size of the population, that’s exponential growth. Part one: Two ways to understand exponential growth We will see in this article that exponential growth doesn’t have a speed: it is the way the speed keeps changing that is important. Something is “fast” if it has a high speed. It has been commented that “exponential” growth is often taken to be a synonym for “fast” growth. This article is for readers who are increasingly familiar with the term “exponential growth”, for example from news coverage of the covid-19 pandemic, and would like a non-mathematical explanation Exponential growth: what it is, why it matters, and how to spot it
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |