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

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.

Athenalsun Athenalsun · Answer 2 · 2020-11-22T04:05:55+01:00

Answer:

2009

Explanation:

After one year, there will be 60% left. After two years, there will be 36% left. After three years, there will be 21.6% left.

As we can see, these are just increasing powers of 60%, the next year will not dip below 10%, because 60% > 50%, and 21.6 > 20. However, without calculating it exactly, you know that it will be less than 16.6%, and thus, it will take 5 years - meaning that in 2009, the total number of wrens will drop below 10% of what it originally was.