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Question: 32 approximate logo 2 by converging on the root of...

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3.2 Approximate log,o 2 by converging on the root of f(x) -10 7 pts 20 BY HAND using the three methods below, actually calculating and tabulating values for x, f(x) and f(x) as appropriate. Do two iterations for each method, accurate to at least 4 decimals. Of course by-hand means you can still use your calculator for all the hard arithmetic (multiplying and dividing), but I want to see all your steps: write out the formulae you are using and key values as you iterate so we can confirm youre doing the process correctly. (i) Bisection: start with the bracket a 0, b 1 and calculate x, and x2, clearly showing how the as and/or bs are changing after both iterations. (ii) Secant: start with x,0, x2-1. Calculate x and x4 (il) N-R start with x1. Calculate x2 and x Using the exact value x = log102 = 0.30103, compare the error in the final iteration of X between all three methods and rank how well each did for this case (worst to best) 3.3 The growth model of a production hog is given by 3 logow 0.5t-0.05 w, where w is the hogs weight (in lbs) by the time its t days old. You just care about the weight (w of a 30-day old hog (i.e. just at t30), but the non-linear equation for w is too hard to solve for w directly. 2 pts Write this problem in the generic fx) O form for the case t 30. Thats it! Im just asking you to complete the physics step-dont actually solve for w! Just write the initial fx) equation, ready to solve for the hogs weight using any of the Chapter 3 methods later.

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