Chapter 11.3, Problem 92E

Biology-Reproduction Another model, the predator satiation model for population growth, specifies that the reproductive rate of an organism as a function of the total population varies according to the following formula:

$R\left(p\right)=\frac{rp}{1+kp},$ where p is the total population in thousands of organisms, r and k are constants that depend on the particular circumstances and the organism being studied, and $R\left(p\right)$ is the reproduction rate in thousands of organisms per hour. $k=0.2\text{ and }r=0.08,$, find $R\text{'}\left(p\right)$

and $R\text{'}\left(2\right)$. Interpret the result.