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Official unemployment rates for the U.S. population are reported on a monthly basis by the Bureau of Labor Statistics. For the period October, 2011, through January, 2012, the official unemployment rates were 8.9% (Oct.), 8.7% (Nov.), 8.5% (Dec.), and 8.3% (Jan.). (Source: U.S. Bureau of Labor Statistics, www.bls.gov.) If the unemployment rates were to continue to decrease following a linear model, (a) predict the unemployment rate on January, 2013. (b) predict when the United States would reach a zero unemployment rate.

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Step-by-step explanation:

Clearly, there is a common difference between the monthly employment rates:

8.7% - 8.9% = -0.2%

8.5% - 8.7% = -0.2%

8.3% - 8.5% = -0.2%

a) So, for every month x, the percentage will go down 0.2%, starting at 8.9%. So, we can make this equation:

y = -0.2x + 9.1, where x = 1 would be October 2011.

January 2013 is 16 months after October 2011, so:

y = -0.2(16) + 9.1

y = 5.9%

b) To find when the unemployment rate will be zero, we set the equation equal to zero:

0 = -0.2x + 9.1

-0.2x = -9.1

x = 45.5 months

So, rounding up, the U.S. would reach a zero unemployment rate in 46 months or around September 2014? Not completely sure.

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