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?