1. The number of new infections produced by an individual infected with a pathogen depends on the pathogen-induced mortality rate, referred to as the pathogen's virulence. Suppose that new infections N as a function of virulence v can be modeled as N (v) = (a) Find lim, N (v). Show your steps. (b) Interpret your answer to part (a) in the context of the model. (c) Determine the virulence v at which new infections N is maximized. Use the first derivative test to verify your answer. 8v 1+2v+v²¹ v> 0.

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