8.6. The exercise considers fitting data using the model function g(x) = v12 2, which is known as a power law function, and also as an allometric function. Two different methods are considered, one summarized in (a) and (b), and the second in (c) and (d). Assume that the data are (21, y1), (12, y2), . . . , (In, Un), where the ci's and yi's are positive. (a) Writing y = v1272, and then taking the log of this equation, show that the transformed model function can be written as G(X ) = Vi + V2X, where Vi = logo and V2 = v2. Also, show that the transformed data points (Xi, Yi) are Xi = log x; and Yi = log yi. (b) Continuing from part (a), using the least squares error E(V1, V2) = E(Vi + V2Xi - Yi), and the common log, show that v1 = 10 4 and v2 = V2, where Vi and V2 are given in (8.31). (c) Show that to minimize the error function E(v1, v2) = _(via;2 -yi), one gets that U1 = (d) Continuing from part (c), show that finding the minimum of E(v1, v2) reduces to solving an equation of the form F(v2) = 0. Write down the function F, and explain why the secant method might be easier to use to solve the equation than Newton's method