$**$Use MatLab$**$

An investigator has reported the data tabulated below for an experiment to determine the growth rate of bacteria $k($per day$)$ as a function of oxygen concentration $c(m\frac{g}{L}).$ It is known that such data can be modeled by the following equation:

$k=\frac{k_{\text{m}\text{a}\text{x}}{c}^2}{c_s+c^2}$

where $c_s$ and $k_{\text{m}\text{a}\text{x}}$ are parameters. Use a transformation to linearize this equation. Then use linear regression to estimate $c_s$ and $k_{\text{m}\text{a}\text{x}}$ and predict the growth rate at $c=2m\frac{g}{L}.[20$ pts$]$

$\backslash$table$[[c,0\mathrm{.}5,0\mathrm{.}8,1\mathrm{.}5,2\mathrm{.}5,4],[k,1\mathrm{.}1,2\mathrm{.}4,5\mathrm{.}3,7\mathrm{.}6,8\mathrm{.}9]]$