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Formula $f(n)=k-k(1-\frac{1}{k})^n$ has $k$ as a constant. Function $f(n)$ shall be a measure of confidence. How can we best describe the growth of confidence with every $n$ in a few words?

A plot of the formula: $k=50$

E.g. exponential decay seems to be linked to Euler's constant $e$. What might be the best English to express the growth of $f(n)$ with $n$? Why?

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If you want the description to refer specifically to the growth of confidence (and not just describe the function or the shape of the graph), this might be better suited for stats.stackexchange.com? –  joriki Dec 10 '11 at 8:30

1 Answer 1

"Exponential decay" is the phrase you want. If $k$ is a constant, you can write $k-k(1-\frac{1}{k})^n$ as $k-ke^{-\lambda n}$ for some $\lambda$, and you should be able to find that $\lambda$.

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