Math in the News: Issue 94

Math in the NewsIssue 94

Winter’s Impact on Florida’s Orange Crop

Florida’s Orange CropFor 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 CropWhen 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 CropOver 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 CropHere is the data for orange production in Florida for the growing seasons from 2001 to 2012. Input this data into a spreadsheet. Create a third column to calculate the percent change.

Year Tons (1000's)2001-2002 727.6

2002-2003 718.1

2003-2004 679

2004-2005 641.4

2005-2006 576.4

2006-2007 554.4

2007-2008 538.9

2008-2009 530.9

2009-2010 517.1

2010-2011 503.6

2011-2012 495.1

Florida’s Orange CropLet’s measure the percentage drop in output over the past few years. Use this formula for percent increase and decrease.

Florida’s Orange CropInput a spreadsheet formula for calculating the percent change. Use a variation of this formula:

=(B2-B1)/B1

Format the output as a percent.

Year Tons (1000's)

Percent Change

2001-2002 727.6 --

2002-2003 718.1 -1.31%

2003-2004 679 -5.44%

2004-2005 641.4 -5.54%

2005-2006 576.4 -10.13%

2006-2007 554.4 -3.82%

2007-2008 538.9 -2.80%

2008-2009 530.9 -1.48%

2009-2010 517.1 -2.60%

2010-2011 503.6 -2.61%

2011-2012 495.1 -1.69%

Florida’s Orange CropSince its big drop in crop production in 2005, there has been an average drop of 2.5% each subsequent year.

Year Tons (1000's)

Percent Change

2005-2006 576.4 -10.13%

2006-2007 554.4 -3.82%

2007-2008 538.9 -2.80%

2008-2009 530.9 -1.48%

2009-2010 517.1 -2.60%

2010-2011 503.6 -2.61%

2011-2012 495.1 -1.69%

Avg -2.5%/yr

Florida’s Orange CropThe change in output from 2005 to 2012 is the product of each year’s net percentage.

A reasonable estimate is found using the average percent change.

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

Florida’s Orange CropThe Florida Department of Citrus—http://fdocgrower.com—estimates a 4% to 8% drop in orange production over the next few years. Let’s see what that could look like. Let’s use our previous spreadsheet data.

Year Tons (1000's)

Percent Change

2005-2006 576.4 -10.13%

2006-2007 554.4 -3.82%

2007-2008 538.9 -2.80%

2008-2009 530.9 -1.48%

2009-2010 517.1 -2.60%

2010-2011 503.6 -2.61%

2011-2012 495.1 -1.69%

Florida’s Orange CropTake the last data point and estimate the output five years out for the two percentage drops.

Florida’s Orange CropUse these expressions to find the potential number of tons of oranges not produced over the next five years.

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.