An interesting biological experiment (see [Schr2]) concerns the determination of the maximum water temperature, XM, at which various species of hydra can survive without shortened life expectancy. One approach to the solution of this problem uses a weighted least squares fit of the form f (x) = y = a/(x − b)c to a collection of experimental data. The x-values of the data refer to water temperature. The constant b is the asymptote of the graph of f and as such is an approximation to XM.
a. Show that choosing a, b, and c to minimize


reduces to solving the nonlinear system


b. Solve the nonlinear system for the species with the following data. Use the weights wi = ln yi.