Continuing from his previous post, the tutor assesses whether the sequoia tree’s growth is exponential.  Normally, tutoring doesn’t encompass this topic; it’s interesting nonetheless.

 
Growing 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?

Based on computations similar to the ones shown in my last post, I’ve compiled the following table of (projected) year over year growth percentages:

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%.

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%.

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.

To get the growth rates tabulated above, the tutor used a Perl program 11 lines long. More about that program in a future post:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.