The unemployment rate U(t) varies with time. The table gives the percentage of unemployed in a certain country's labor force from 1999 to 2008. t | U(t) | t | U(t) 1999 | 4.3 | 2004 | 5.5 2000 | 4.1 | 2005 | 5.1 2001 | 4.7 | 2006 | 4.6 2002 | 5.6 | 2007 | 4.6 2003 | 6.3 | 2008 | 5.6 (a) What is the meaning of U'(t)? - The derivative U'(t) is the percentage of people who are unemployed at a given time. - The derivative U'(t) is the rate at which people are being fired with respect to time. - The derivative U'(t) is the rate at which the unemployment rate is changing with respect to time. - The derivative U'(t) is the number of people who are unemployed at a given time. What are its units? - percent unemployed per year - percent unemployed - people - people per year (b) Construct a table of values for U'(t). (Use h = 1 for 1999 and h = -1 for 2008. For all other years, use h = -1 and h = 1.) t | U'(t) | t | U'(t) 1999 | | 2004 | 2000 | | 2005 | 2001 | | 2006 | 2002 | | 2007 | 2003 | | 2008 |
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- U(1999) = 0.0 - U(2000) = 0.0 - U(2001) = 2.0 - U(2002) = 4.6 - U(2003) = 4.6 - U(2004) = 4.6 - U(2005) = 4.6 - U(2006) = 4.6 - U(2007) = 4.6 - U(2008) = 0.0 Show more…
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The unemployment rate $U(t)$ varies with time. The table (from the Bureau of Labor Statistics) gives the percentage of unemployed in the US labor force from 1999 to 2008 . $$\begin{array}{|c|c|c|c|}\hline t & {U(t)} & {t} & {U(t)} \\ \hline 1999 & {4.2} & {2004} & {5.5} \\ {2000} & {4.0} & {2005} & {5.1} \\ {2001} & {4.7} & {2006} & {4.6} \\ {2002} & {5.8} & {2007} & {4.6} \\ {2003} & {6.0} & {2008} & {5.8} \\ \hline\end{array}$$ (a) What is the meaning of $U^{\prime}(t) ?$ What are its units? (b) Construct a table of estimated values for $U^{\prime}(t)$ .
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The unemployment rate U(t) varies with time. The table (from the Bureau of Labor Statistics) gives the percentage of unemployed in the US labor force from 1993 to 2002. $$\begin{array}{|c|c|c|c|}\hline t & {U(t)} & {t} & {U(t)} \\ \hline 1993 & {6.9} & {1998} & {4.5} \\ {1994} & {6.1} & {1999} & {4.2} \\ {1995} & {5.6} & {2000} & {4.0} \\ {1996} & {5.4} & {2001} & {4.7} \\ {1997} & {4.9} & {2002} & {5.8} \\ \hline\end{array}$$ (a) What is the meaning of $U^{\prime}(t) ?$ What are its units? (b) Construct a table of values for $U^{\prime}(t).$
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