Chapter 17, Problem 12P

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

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

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 $c=2\text{mg/L}$.

c	0.5	0.8	1.5	2.5	4
y	1.1	2.4	5.3	7.6	8.9