Math in the News: Issue 94

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Published on March 2, 2014

Author: Media4Math

Source: slideshare.net

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In this issue of Math in the News we look at the impact of a harsh winter on Florida's orange crop. In addition we look at an ongoing problem that orange production has had with a crop infestation. This provides opprotunities to apply percent change formulas to real-world data.

Winter’s Impact on Florida’s Orange Crop Math in the News Issue 94

Florida’s Orange Crop For the past few years, Florida’s orange crop had been struggling, due to a crop infestation. This winter’s Polar Vortex effect has put more pressure on this crop. In this issue we look at the long-term prospects for Florida’s orange crop.

Florida’s Orange Crop When it comes to orange production in the US, Florida is king. This graph shows the overall US production and Florida’s contribution to that total. (Source: USDA.)

Florida’s Orange Crop Over the past few years Florida’s production of oranges has dropped. This has been due to an infestation of the Asian psyllid, an insect that transmits a bacterium that causes oranges to fall from the tree long before they’re mature. It was first detected in 2005.

Florida’s Orange Crop Here is the data for orange production in Year Florida for the growing seasons from 2001 to 2012. Input this data into a spreadsheet. Create a third column to calculate the percent change. Tons (1000's) 2001-2002 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007 2007-2008 2008-2009 2009-2010 2010-2011 2011-2012 727.6 718.1 679 641.4 576.4 554.4 538.9 530.9 517.1 503.6 495.1

Florida’s Orange Crop Let’s measure the percentage drop in output over the past few years. Use this formula for percent increase and decrease. Year2 - Year1 Percent Change = ´ 100% Year1

Florida’s Orange Crop Input a spreadsheet Tons formula for Year (1000's) calculating the 2001-2002 727.6 percent change. Use 2002-2003 718.1 a variation of this 2003-2004 679 2004-2005 641.4 formula: 2005-2006 576.4 =(B2-B1)/B1 2006-2007 554.4 Format the output as 2007-2008 538.9 a percent. 2008-2009 530.9 2009-2010 2010-2011 2011-2012 517.1 503.6 495.1 Percent Change --1.31% -5.44% -5.54% -10.13% -3.82% -2.80% -1.48% -2.60% -2.61% -1.69%

Florida’s Orange Crop Since its big drop in crop production in 2005, there has been an average drop of 2.5% each subsequent year. Year 2005-2006 2006-2007 2007-2008 2008-2009 2009-2010 2010-2011 2011-2012 Tons Percent (1000's) Change 576.4 554.4 538.9 530.9 517.1 503.6 495.1 -10.13% -3.82% -2.80% -1.48% -2.60% -2.61% -1.69% Avg 2.5%/yr

Florida’s Orange Crop The change in output from 2005 to 2012 is the product of each year’s net percentage. 576 • (1- 0.0383)(1- 0.028)(1- 0.0148)(1- 0.026)(1- 0.0261)(1- 0.0169) = 494.68 A reasonable estimate is found using the average percent change. 576 • (1- 0.025)6 = 479.79

Florida’s Orange Crop While crops have been in decline, the Winter of the Polar Vortex has put the current season’s harvest in further jeopardy.

Florida’s Orange Crop The Florida Tons Year Department of (1000's) 2005-2006 576.4 Citrus— 2006-2007 554.4 http://fdocgrower.co 2007-2008 538.9 m—estimates a 4% 2008-2009 530.9 to 8% drop in orange 2009-2010 517.1 production over the 2010-2011 503.6 next few years. Let’s 2011-2012 495.1 see what that could look like. Let’s use our previous spreadsheet data. Percent Change -10.13% -3.82% -2.80% -1.48% -2.60% -2.61% -1.69%

Florida’s Orange Crop Take the last data point and estimate the output five years out for the two percentage drops. Output (4% drop/year) = 495.1• (0.96)5 = 403.7 Output (8% drop/year) = 495.1• (0.96)5 = 326.3

Florida’s Orange Crop Use these expressions to find the potential number of tons of oranges not produced over the next five years. 4 (495.1•(0.96)i ) • 0.04 å i=0 4 (495.1•(0.96)i ) • 0.08 å i=0

Florida’s Orange Crop • What is the potential loss in the orange crop over the next five years? • Estimate how many oranges this is. • Estimate the volume this number of oranges would take up.

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