## Concave Growth Function

This is for my homies taking calculus.

Here’s a real-life example of a **concave function**. Around minute 35, they say that **as an animal grows in size, each cell requires less energy** — so its total energy consumption is concave as a function of size.

Yup, this is the complicated way to say it — on purpose. Listen to the podcast to hear it in terms of **elephants and mice**.

I think there is an even more complicated way to put it — maybe it’s called the “Euler characteristic” or something, essentially it’s that

so that different functions with a different value for **n** scale in different ways.

If you can put the symbols together with the real-life meaning, it will pay off in terms of insight. You can see something and think to yourself “hey, that’s convex!” And you can also imagine the phenomenon with a different value of **n** — i.e. different scaling properties.

Tags: calculus, concave, function, math, scaling properties, science

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