Answer to Question #158020 in Calculus for Cypress

Question #158020

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?


1
Expert's answer
2021-02-02T05:22:55-0500

limx+10x1+0.1x=limx+100.1+x1=limx+1001+10x1=100\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.


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