Chapter 2.4, Problem 67E

Environment The model

$P\text{ = }\frac{t^2-t+1}{t^2+\text{ 1}}$ measures the percent P (in decimal form) of the normal level of oxygen in a pond, where t is the time (in weeks) after organic waste is dumped into the pond. Find the rate of change of $\text{P at }\left(\text{a}\right)t\text{ = 0}\text{.5, }\left(\text{b}\right)t\text{ = 2, and }\left(\text{c}\right)t\text{ =8}\text{.}$

Interpret the meaning of these values.