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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 – joriki Dec 10 '11 at 8:30

"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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