3 ms·

I'm confused with the math used here. I think exponential is something like you double the height, and quadruple the costs. And that doesn't sound unrealistic t

by nosse 15y ago

I'm confused with the math used here. I think exponential is something like you double the height, and quadruple the costs. And that doesn't sound unrealistic to me.

ScottBurson 15y ago
I'm sure nontechnical people use the term "exponential" loosely, but this being HN, I think clarification is in order. Consider the function f(x) = x ^ 2 (where the caret stands for exponentiation, of course). This is called a quadratic function. Here are some example values: 0 1 2 3 4 5 6 7 8 9 0 1 4 9 16 25 36 49 64 81 This is the kind of relationship you have described: when x is doubled, f(x) is quadrupled. Now consider this function: f(x) = 2 ^ x This is an example of a function that is properly called exponential. Here are some example values: 0 1 2 3 4 5 6 7 8 9 1 2 4 8 16 32 64 128 256 512 Here, every time x increases by 1, the value is doubled. See how much faster it grows? In very practical terms, the difference between a "power law", as functions of the form x ^ k are called, and an exponential, of the form k ^ x, is massive. I grant that the terminology may be a little confusing, but this is not a pedantic distinction!
- nosse 15y ago
  I'm sorry I didn't get that right. I should studying where I study. Anyhow I don't think "50 more and double the cost's" is exponential? // And I still would not think exponential is impossible function for the cost's. When you get about one kilometer high, the stuff just gets shit expensive. I mean humankind-scale expensive.
  - sesqu 15y ago
    "50 more and double the costs" is exponential; in particular, it's cost(height) = reference_cost × 2^((height-reference_height)/50), or simply cost(height) = k × 1.01395948^height.
pavpanchekha 15y ago
Nope. When something is exponential, a fixed increase in the input causes a multiplier in the output. So, for example, if I have the exponential y = 2^x, an increase of 1 in x, from x to x+1, increases y by a factor of two.

by nosse 15y ago

I'm confused with the math used here. I think exponential is something like you double the height, and quadruple the costs. And that doesn't sound unrealistic to me.

ScottBurson 15y ago

I'm sure nontechnical people use the term "exponential" loosely, but this being HN, I think clarification is in order. Consider the function f(x) = x ^ 2 (where the caret stands for exponentiation, of course). This is called a quadratic function. Here are some example values: 0 1 2 3 4 5 6 7 8 9 0 1 4 9 16 25 36 49 64 81 This is the kind of relationship you have described: when x is doubled, f(x) is quadrupled. Now consider this function: f(x) = 2 ^ x This is an example of a function that is properly called exponential. Here are some example values: 0 1 2 3 4 5 6 7 8 9 1 2 4 8 16 32 64 128 256 512 Here, every time x increases by 1, the value is doubled. See how much faster it grows? In very practical terms, the difference between a "power law", as functions of the form x ^ k are called, and an exponential, of the form k ^ x, is massive. I grant that the terminology may be a little confusing, but this is not a pedantic distinction!

nosse 15y ago
I'm sorry I didn't get that right. I should studying where I study. Anyhow I don't think "50 more and double the cost's" is exponential? // And I still would not think exponential is impossible function for the cost's. When you get about one kilometer high, the stuff just gets shit expensive. I mean humankind-scale expensive.
- sesqu 15y ago
  "50 more and double the costs" is exponential; in particular, it's cost(height) = reference_cost × 2^((height-reference_height)/50), or simply cost(height) = k × 1.01395948^height.

pavpanchekha 15y ago

Nope. When something is exponential, a fixed increase in the input causes a multiplier in the output. So, for example, if I have the exponential y = 2^x, an increase of 1 in x, from x to x+1, increases y by a factor of two.