Assign 5 - MATH 1330D Winter 2014 Assignment 5 Due Thursday March 20 at 7pm Late assignments will not be accepted 1 Consider the equation ln x = x 3(a

# Assign 5 - MATH 1330D Winter 2014 Assignment 5 Due Thursday...

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MATH 1330D, Winter 2014, Assignment 5 Due Thursday March 20 at 7pm Late assignments will not be accepted 1. Consider the equation lnx=x3(a) Use the intermediate value theorem to convince yourself that the equation has apositive solution and find a reasonable guess.(b) Use Newton’s method to update your guess twice.2. Suppose a bacterium enhances its own per capita production, which is given byper capita production = r(1 +btK)wherebtis the population size at timet,r= 0.5 andK= 10(a) Graph per capita production as a function of population size.(b) Find the DTDS for the population and graph the updating function for thispopulation.(c) Find the equilibrium of the DTDS for the population.(d) Find the stability of the equilibrium by the derivative.3. Consider a population following the updating function