Question

For a particular predator-prey relationship, it was determined that the number y of prey consumed by an individual predator over a period of time was a function of the prey density x (the number of prey per unit area). Suppose that y=f(x)=(10x)/(1+0.1x)

If the prey density were to increase without bound, what value would y approach?

Answer 1

$\lim\limits_{x\to+\infty}\frac{10x}{1+0.1x}=\lim\limits_{x\to+\infty}\frac{10}{0.1+x^{-1}}=\lim\limits_{x\to+\infty}\frac{100}{1+10x^{-1}} = 100$

Therefore, the number of prey consumed by an individual predator over a period of time approaches to 100, when the prey density increases unboundly.