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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?

 Feb 9, 2021

Best Answer 

 #1
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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 = .6n 

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?

 Feb 9, 2021
 #1
avatar
+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 = .6n 

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

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