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?

I thought the answer was 2008 but it is wrong. Can someone help me please?

Guest Feb 9, 2021

#1**+1 **

Let's say there is 100 to start with (as in 100%)

10 = 100 (1-.4)^{n} where n is the number of years after 2004 to reach 10%

10/100 = (1-.4)^{n}

.1 = .6^{n}

log .1 = n log .6

n = 4.51 years to reach 10%

this will be in VERY late 2008 but I bet they say it is 2009 because it askes what year the census will show <10%......there will be no new census until 2009 ....... kinda tricky, huh?

Guest Feb 9, 2021

#1**+1 **

Best Answer

Let's say there is 100 to start with (as in 100%)

10 = 100 (1-.4)^{n} where n is the number of years after 2004 to reach 10%

10/100 = (1-.4)^{n}

.1 = .6^{n}

log .1 = n log .6

n = 4.51 years to reach 10%

this will be in VERY late 2008 but I bet they say it is 2009 because it askes what year the census will show <10%......there will be no new census until 2009 ....... kinda tricky, huh?

Guest Feb 9, 2021