Question

75 POINTS IF U GET THIS RIGHT !!!!!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?

Answer 1

2009

Explanation:

On June 1, 2004 we can say that there were 100% of the wrens.

If the number decreases by 40% each year, then each year there will be 60% of the previous years number. To find 60%, multiply by 0.6 (since 60% = 60/100 = 0.6)

June 1, 2004 = 100%

June 1, 2005 = 100% x 0.6 = 60%

June 1, 2006 = 60% x 0.6 = 36%

June 1, 2007 = 36% x 0.6 = 21.6%

June 1, 2008 = 21.6% x 0.6 = 12.96%

June 1, 2009 = 12.96% x 0.6 = 7.776%

Therefore, the census shows that the number of wrens is less than 10% in the year 2009.

Answer 2

In 2009

Explanation:

If the wren population is going down by 40% each year, that means the following year's population is just 60% of what was in the previous year. This means that what we have to do is multiply the previous year's number by 0.6 to get the current year's population. If we take the data from 2004 as 100%, we have the following numbers:

2004 = 100%

2005 = 60 % (100 * .6)

2006 = 36 % (60 * .6)

2007 = 21.6 % (36 * .6)

2008 = 12.96 % (21.6 * .6)

2009 = 7.776% (12.96 * .6)

This means that 2009 will show that the wren population is less than 10% (7.776%) than what it was in the year 2004.

I hope this helps! :D