Answer
(a) $f(8) = 12, 820$
(b) $g(8) = 12,729$
(c) The exponential model is a better model for the data in 2008.
Work Step by Step
(a) The linear model $f(x) = 782x + 6564$ predicts that, in the year 2008, $x = 2008 - 2000 = 8$. Therefore: $$f(8) = 782(8) + 6564$$ $$f(8) = 6256 + 6564$$ $$f(8) = 12, 820$$
(b) The exponential model $g(x) = 6875e^{0.077x}$ predicts that, in the year 2008, $x = 2008 - 2000 = 8$. Therefore: $$g(8) = 6875e^{0.077(8)} = 687e^{0.616} \approx 12,729$$
(c) When comparing the values from (a) and (b) with the graph of the average cost of family insurance for the year 2008, we see that both are good models for the values in the graph, but the exponential model more closely resembles the average reported.
