Answer
(a) $f(11) = 15,166$
(b) $g(11) = 17, 627$
(c) The linear function $f(x) = 782x + 6564$ is a better model for the data in 2011.
Work Step by Step
(a) The linear model $f(x)=782x + 6564$ for the cost of insurance predicts that, in 2,011, $x = 2011 - 2000 = 11$. Therefore: $$f(11)_{Insurance} = 782(11) + 6564 = 15,166$$
(b) The exponential model $g(x) = 687e^{0.077x}$ for the cost of insurance predicts that, in 2,011, $x = 2011 - 2000 = 11$. Therefore: $$g(11) = 687e^{0.077(11)}$$ $$g(11) = 687e^{0.847} \approx 17,627$$
(c) When we look at the graph, we see that the average cost of family health insurance for 2,011 was $15,073$ dollars. Of the two models presented, we see that the one that more closely resembles the reported average is the linear model.
