The saturation concentration of dissolved oxygen in fresh-water can be calculate with the equation

Where O_s??= the saturation concentration of dissolved oxygen in freshwater at l atm (mg/L) and T_a?= absolute temperature (K). Remember that T_a = T + 273.15, where T = temperature (^oC).According to this equation, saturation decreases with increasing temperature. For typical natural waters in temperate climate, the equation can be used to determine that oxygen concentration ranges from 14.621 mg/L at 0^oC to 6.413 mg/L at 40^oC. Given a value of oxygen concentration, this formula and the bisection method can be used to solve for temperature in ^oC.

(a) If the initial guesses are set as 0 and 40^oC, how many bisection iterations would be required to determine temperature to an absolute error of 0.05^oC?

(b) Develop and test a bisection program to determine T as a function of a given oxygen concentration to a prespecified absolute error as in (a). Given initial guesses of 0 and 40^oC, test your program for an absolute error = 0.05^oC and the following cases: o_sf = 8, 10 and 12 mg/L. Check your results.

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1.575701 x 10 6.642308 x 10" T? 8.621949 x 10" In o,f = -139.34411 + -139.344 11+ 1.243800 x 1010