Question: Consider the non-linear first order difference equation:xn+1=exn+ln(xn+1)-2Solving for the steady state of this equation in its current form is basically impossible. Instead, let us replace

Consider the non-linear first order difference equation:xn+1=exn+ln(xn+1)-2Solving for the steady state of this equation in its current form is basically "impossible". Instead, let us replace ex+ln(x+1)-2 with itssecond degree Taylor polynomial, T2(x) centered atx=0.Ifwedo this then:T2(x)=Ifwe then plug in and write xn+1~~T2(xn),we can solve for an approximation ofxbasedon our presumably correct approximationfunction.x=Using graphing software, find the real steady state for this difference equation. Is our current approximation an under or over estimate ofthe true value?

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