The Concentration $C$ (In Parts Per Million) of Carbon Dioxide in the Atmosphere

question 40

Multiple Choice

The concentration $C$ (in parts per million) of carbon dioxide in the atmosphere is measured at the Mauna Loa Observatory in Hawaii. The greatest monthly carbon dioxide concentration for each year from 2002 to 2006 is shown in the table. $$\begin{array} { | c | c | c | } \hline \text { Year } & t & \text { Concentration, } C \\\hline 2002 & 0 & 375.55 \\\hline 2003 & 1 & 378.35 \\\hline 2004 & 2 & 380.63 \\\hline 2005 & 3 & 382.26 \\\hline 2006 & 4 & 384.92 \\\hline\end{array}$$ Solve the following system for $a$ and $b$ to find the least squares regression line $y = a t + b$ for the data. Let $t$ represent the year, with $t = 0$ corresponding to 2002. $$\left\{ \begin{array} { r } 5 b + 10 a = 1901.71 \\10 b + 30 a = 3826.07\end{array} \right.$$ Use the least square regression line to predict the largest monthly carbon dioxide concentration in 2011. Round your answer to the nearest hundredths part per million.

• A)402.99 parts per million
• B)387.14 parts per million
• C)400.73 parts per million
• D)393.93 parts per million
• E)396.20 parts per million

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