\nGrowing a foot (in height) per year, the tree is growing arithmetically, rather than exponentially. Arithmetic growth is annual increase by a constant amount; exponential growth is annual increase by a constant percentage. However, since growth is increase in mass, could exponential growth model the tree’s progress, even if its growth is not, technically speaking, exponential?<\/p>\n
Based on computations similar to the ones shown in my last post,<\/a> I’ve compiled the following table of (projected) year over year growth percentages:<\/p>\n
| year<\/th>\n | percentage growth<\/th>\n<\/tr>\n |
|---|---|
| now (2014)<\/td>\n | na<\/td>\n |
| 2015<\/td>\n | 3.03<\/td>\n<\/tr>\n |
| 2016<\/td>\n | 3.00<\/td>\n<\/tr>\n |
| 2017<\/td>\n | 2.97<\/td>\n<\/tr>\n |
| 2018<\/td>\n | 2.94<\/td>\n<\/tr>\n |
| 2019<\/td>\n | 2.91<\/td>\n<\/tr>\n |
| 2020<\/td>\n | 2.88<\/td>\n<\/tr>\n |
| 2021<\/td>\n | 2.86<\/td>\n<\/tr>\n |
| 2022<\/td>\n | 2.83<\/td>\n<\/tr>\n |
| 2023<\/td>\n | 2.80<\/td>\n<\/tr>\n |
| 2024<\/td>\n | 2.78<\/td>\n<\/tr>\n |
| 2025<\/td>\n | 2.75<\/td>\n<\/tr>\n |
| 2026<\/td>\n | 2.73<\/td>\n<\/tr>\n |
| 2027<\/td>\n | 2.70<\/td>\n<\/tr>\n |
| 2028<\/td>\n | 2.68<\/td>\n<\/tr>\n |
| 2029<\/td>\n | 2.65<\/td>\n<\/tr>\n |
| 2030<\/td>\n | 2.63<\/td>\n<\/tr>\n |
| 2031<\/td>\n | 2.61<\/td>\n<\/tr>\n |
| 2032<\/td>\n | 2.59<\/td>\n<\/tr>\n |
| 2033<\/td>\n | 2.56<\/td>\n<\/tr>\n |
| 2034<\/td>\n | 2.54<\/td>\n<\/tr>\n<\/table>\n From the table, we see that the tree’s growth is not exponential; if it were, the rate would be the same from year to year. However, for any given span of 3 to 4 years, its rate will likely not change by more than 0.1%; for any span of 10 years, by likely not more than 0.25%.<\/p>\n The implication is that, for example, if you notice the tree’s year-over-year growth is 2.5%, you could fairly confidently model its growth over the next 20 years at 2.3% per year. Following the slowly decreasing growth pattern tabulated above (starting with 2.5% per year), you’ll arrive at cumulative growth for the next 20 years of around 57.6%. Similarly, estimating the entire 20 year growth at 2.3% per year gives cumulative growth of 57.6%.<\/p>\n Although the tree’s growth isn’t exponential by definition, it can be modeled fairly accurately by exponential growth. Knowing this year’s rate, you might just need to average it down a bit depending on the time span of your outlook.<\/p>\n To get the growth rates tabulated above, the tutor used a Perl program 11 lines long. More about that program in a future post:)<\/p>\n |