By using U.S. Energy Information Administration data from 2012 and projected to 2040, the total U.S. employment in manufacturing, E in millions, can be modeled by

E(t) = 0.0052t2 + 0.080t + 12

Were t is the number of years past 2010.

(a) In what year does the model predict that manufacturing employment will be at its maximum, and what is that maximum?

(b) When does the model predict that manufacturing employment will be 11.5 million?