Answer
(a) $U'(t)$ is the rate of change of the percentage of unemployed and it is measured in units of percentage per year.
(b) We can estimate the values for $U'(t)$:
2003: $U'(t) = -0.50$
2004: $U'(t) = -0.45$
2005: $U'(t) = -0.45$
2006: $U'(t) = -0.25$
2007: $U'(t) = 0.60$
2008: $U'(t) = 2.35$
2009: $U'(t) = 1.90$
2010: $U'(t) = -0.20$
2011: $U'(t) = -0.75$
2012: $U'(t) = -0.80$
Work Step by Step
(a) $U'(t)$ is the rate of change of the percentage of unemployed and it is measured in units of percentage per year.
(b) We can estimate the values for $U'(t)$:
2003: $U'(t) = \frac{5.5-6.0}{1} = -0.50$
2004: $U'(t) = \frac{5.1-6.0}{2} = -0.45$
2005: $U'(t) = \frac{4.6-5.5}{2} = -0.45$
2006: $U'(t) = \frac{4.6-5.1}{2} = -0.25$
2007: $U'(t) = \frac{5.8-4.6}{2} = 0.60$
2008: $U'(t) = \frac{9.3-4.6}{2} = 2.35$
2009: $U'(t) = \frac{9.6-5.8}{2} = 1.90$
2010: $U'(t) = \frac{8.9-9.3}{2} = -0.20$
2011: $U'(t) = \frac{8.1-9.6}{2} = -0.75$
2012: $U'(t) = \frac{8.1-8.9}{1} = -0.80$
