Great minds think a like!

That’s a really good explanation for the exponential function. I think I’ll update the post and add it when I have a bit more time.

]]>For exponential functions, the definition of an exponential function is that f(x + k) = cf(x) – an additive increment in x causes a multiplicative increase in f(x). Consider multiplying rabbits: year 1, you have 100 rabbits. Year 2 (simplifying here and making rabbits immortal and instantly adult for the sake of example) each rabbit pair has 2 children (ie. 1 child per rabbit), so 100 rabbits get added and you have 200 rabbits. Year three, add 200, get 400. The pattern is that the rate of growth is clearly a multiple of the population itself (in our case 1x, for dogs we might make it 0.1x), and an increment of 1 year doubles the population (or, in dogs, increases it by 1.1x).

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