Chapter 4.1, Problem 94E

Air Pollution The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in the city of Long Beach is approximated by

$A(t)=\frac{136}{1+0.25{\left(t-4.5\right)}^2}+28$ (0 ≤ t ≤ 11)

where A(t) is measured in pollutant standard index (PSI) and t is measured in hours, with t = 0 corresponding to 7 a.m. Find the intervals where A is increasing and where A is decreasing, and interpret your results.

Source: Los Angeles Times.