Recycled Material Year Thousand Tons 2000 80 2003 90 2006 104 2007 120 2008 132 2009 145 2011 180 (a) Find the quadratic function for the model of the data that gives the yearly amount of material recycled, where \(x\) is the year since 2000, with data from \(0 \leq x \leq 11\). (Round all numerical values to three decimal places.) t(x) = (b) Write the slope formula for the model of the data. t'(x) = (c) How rapidly was the amount of recycled material increasing in 2010? thousand tons per year (d) Does the model have any relative or absolute extrema for years between (and including) 2000 and 2011? (Enter your answers as comma-separated lists. Round your answers to one decimal place. If an answer does not exist, enter DNE.) relative maximum thousand tons relative minimum thousand tons absolute maximum thousand tons absolute minimum thousand tons
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The given data is the yearly amount of material recycled since 2000. Let's organize it in a table: Year | Amount Recycled (thousand tons) -------------------------------------- 2000 | 180 2003 | ? 2006 | ? 2007 | ? 2008 | ? 2009 | ? 2011 | ? We are missing the Show more…
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It is estimated that 90 billion plastic carry-out bags are produced annually in the United States. In recent years, the number of tons of plastic bags that are recycled has grown exponentially from approximately $80,000$ tons in 1996 to $380,000$ tons in 2007 (Source: Environmental Protection Agency). The following exponential function models the amount recycled, in tons: $$R(x)=80,000(1.1522)^{x}$$ where $x$ is the number of years since $1996 .$ Find the total amount recycled, in tons, in 1999 and in 2007 . Then use the function to estimate the total number of tons that will be recycled in 2012 .
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