Question

1.) Air pollution: According to the South Coast Air Quality Management District, the level of Nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in down town Los Angeles is approximated by


A(t) = (0.03t^3)(t-7)^4 + 60.2


(0< = t < = 7)

where A(t) is measured in pollutant standard index (PSI) and t is measured in hours, with t = 0 corresponding to 7 a.m. At what time of day is the air pollution increasing, and at what time is it decreasing? /use the first derivative/

OR

GDP of a Developing Country: A developing country’s gross domestic product (GDP) from 2000 to 2008 is approximated by the function


G(t) = -0.2t^3 + 2.4t^2 + 60

(0< = t < = 8)


where G(t) is measured in billions of dollars and t = 0 corresponds to 2000. Show that the growth rate of the country’s GDP was maximal in 2004. /use the second derivative/

Answer 1

A is decreasing when A' < 0

The growth rate G' is maximal when its derivative (G") is zero.

Just as G has a max when G' = 0.

Answer 2

So, I just plug the numbers (1-7) or (1-8) in for x and make a graph?