Exponent, logarithmic question

Question

I'm reading an article related to bioinformatics and I found this formula: Probability of $x =(1-y/n)^t$ or approximately $e^{-yt/n}$.

My question is how do we pass to the approximation given in the paper: $e^{-yt/n}$ from the initial form:$(1-y/n)^t$.

Answer 1

Take: $$ e^{-yt / n} = \left(e^{-y / n}\right)^t \approx \left( 1 - \frac{y}{n} \right)^t $$ The approximation for $e^{-y/n}$ is just the first two terms of the Taylor expansion.