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?

Firewolf  Jun 10, 2018

Let the number of wrens on June 1, 2004 = W
< 10%W = W x [1 - 0.4]^n, solve for n
<10% = [0.60]^n     take the log of both sides
n = Log(0.099) / Log(0.6)
n = 4.527 years =~4.5 years after 2004.

Guest Jun 10, 2018

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