Every June 1, an ecologist takes a census of the number of wrens in a state park. She noticed that the number is decreasing by $40\%$ each year. If this trend continues, in what year will the census show that the number of wrens is less than $10\%$ of what it was on June 1, 2004

2009

Explanation: It is given that the wren population is going down by 40% each year. This indicates that each following year's population will be 60% of what was in the year preceeding it. To obtain this, multiply the previous year's number by 0.6 (60%) to get the current year's population. Taking the data from 2004 as 100%, the following calculations are obtained:

2004 = 100%

2005 = 60 % (100 × 0.6)

2006 = 36 % (60 × 0.6)

2007 = 21.6 % (36 × 0.6)

2008 = 12.96 % (21.6 × 0.6)

2009 = 7.776% (12.96 × 0.6)

From the above calculations, in 2009 the wren population is 7.776% which is less than 10% of the population that was available in the year 2004.

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