World 1 · Functions & Limits · 8 minExponentials & logs
Growth and its inverse
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An exponential y = a·e^(b·x) grows (or decays) in proportion to its own size — the bigger it is, the faster it changes. It models populations, interest and radioactivity. Its inverse, the logarithm, undoes it: ln turns multiplication into addition.
The number e ≈ 2.718 is special: e^x has slope equal to its height everywhere; so does any constant multiple C·e^x. That self-matching property is why e shows up everywhere in calculus.
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y = a·e^(b·x) with b < 0 describes…
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