Chapter 20, Problem 32P

An environmental engineer has reported the data tabulated below for an experiment to determine the growth rate of bacteria k as a function of oxygen concentration c. It is known that such data can be modeled by the following equation

$k=\frac{k_{\text{max}}{c}^2}{c_s+c^2}$

where $c_s$ and $k_{\max }$ are parameters. Use a transformation to linearize this equation. Then use linear regression to estimate $c_s$ and $k_{\max }$ and predict the growth rate at c = 2mg/L.

$c\left(\text{mg/L}\right)$	0.5	0.8	1.5	2.5	4
$k\left(\text{per day}\right)$	1.1	2.4	5.3	7.6	8.9