$5\mathrm{.}8$ The saturation concentration of dissolved oxygen in

freshwater can be calculated with the equation

$ln{o}_{sf}=-139\mathrm{.}34411+\frac{1\mathrm{.}575701{10}^5}{T_a}$

$-\frac{6\mathrm{.}642308{10}^7}{T_a^2}+\frac{1\mathrm{.}243800{10}^{10}}{T_a^3}$

$-\frac{8\mathrm{.}621949{10}^{11}}{T_a^4}$

where $o_{sf}=$ the saturation concentration of dissolved oxy$-$

gen in freshwater at $1$atm$(mg{L}^{-1})$; and $T_a=$ absolute

temperature $(K).$ Remember that $T_a=T+273\mathrm{.}15,$ where

$T=$ temperature $(C).$ According to this equation, saturation

decreases with increasing temperature. For typical natural

waters in temperate climates, the equation can be used to de$-$

termine that oxygen concentration ranges from $14\mathrm{.}621m\frac{g}{L}$

at $0C$ to $6\mathrm{.}949m\frac{g}{L}$ at $35C.$ Given a value of oxygen con$-$

centration, this formula and the bisection method can be

used to solve for temperature in $C.$

$($a$)$ If the initial guesses are set as $0$ and $35C,$ how many

bisection iterations would be required to determine tem$-$

perature to an absolute error of $0\mathrm{.}05C?$

$($b$)$ Based on $($a$),$ develop and test a bisection M$-$file function

to determine $T$ as a function of a given oxygen concen$-$

tration. Test your function for $o_{sf}=8,10$ and $14m\frac{g}{L}.$

Check your results.

Please solve it using Python.