A company’s number of personnel on active duty (not on sick leave or vacation leave) during the period 2000 - 2013 can be approximated by the cubic model f(x) = 2.5x^3 - 15x^2 - 80x + 1025, where x = 0 corresponds to 2000. Based on the model, how many personnel were on active duty in 2010? What is the domain of f?
If x = 0 corresponds to 2000, when 2010 is 2010 - 2000 = 10. We want f(10):
f(10) = 2.5(10)^3 - 15(10)^2 - 80(10) + 1025
f(10) = 2.5(1000) - 15(100) - 800 + 1025
f(10) = 2500 - 1500 - 800 + 1025
f(10) = 1,225
If x = 0 corresponds to 2000, when 2010 is 2010 - 2000 = 10. We want f(10):
f(10) = 2.5(10)^3 - 15(10)^2 - 80(10) + 1025
f(10) = 2.5(1000) - 15(100) - 800 + 1025
f(10) = 2500 - 1500 - 800 + 1025
f(10) = 1,225