Question Productivity The function defined by fx 01624x 34

Question: Productivity: The function defined by f\'(x) = -0.1624x + 3.4909 approximates marginal U.S. nonfarm productivity from 2000-2009. Productivity is measured as total output per hour compared to a measure of 100 for 2000, and x is the number of years since 2000. a. Give the function that describes total productivity for year x. b. Use your function from part a to find productivity at the end of 2008. In 2009, productivity actually measured 122.3. How does your value using the function compare to this?

a. We have df/dx = f’ (x) = -0.1624x + 3.4909. Therefore, f (x) =1/2 ( -0.1624x²) + 3.4909 x = -0.0812 x² + 3.4909 x. Since the productivity is measured as total output per hour compared to a measure of 100 for 2000, we have, on adding 100, the function that describes total productivity for year x as f(x) = -0.0812 x² + 3.4909 x + 100 where x is the number of years from the year 2000.

b. The productivity at the end of 2008 can be obtained by substituting x = 8 in the above equation. The productivity at the end of 2008 = -0.0812*(8)² + 3.4909(8) + 100 = -0.0812* 64 + 27.9272 +100 = 127.9272- 5.1968 = 122.7304 = 122.7 ( on rounding off to 1 decimal place). For the year 2009, x = 9 so that the productivity at the end of 2009 = - 0.0812*(9)² + 3.4909(9) + 100 = - 6.5772 + 31.4181 + 100 = 131.4181- 6.5772 = 124.8409 = 124.8 ( on rounding off to 1 decimal place)

$Question: Productivity: The function defined by f\'(x) = -0.1624x + 3.4909 approximates marginal U.S. nonfarm productivity from 2000-2009. Productivity is measu$

Question Productivity The function defined by fx 01624x 34

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