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PRE CALC EXPONENTIAL QUES?
Okay the question is:
An endangered species, "cubabears", has a population that is exponentially decreasing. 8 years ago, the population was 1700. Today, there are only 1000 cubabears alive. Once the population hits 100, The cubabears will be considered extinct, and this will be irreversible.
QUESTIONS: How long will it take for this to happen?
I'd appreciate if I got help ASAP seeing as how this is due tomorrow! Thanks in advanceeeee
@Yirmiyahu i dont understand lol
1 Answer
- ?Lv 78 years agoFavorite Answer
Let 8 years ago = time 0
A(t) = Po e ^(-kt)
A(0) = Po = 1700
A(8) = Po e^(-8k) = 1000
e^(-8k) = 1000/1700
k = -1/8 ln(1000/1700)
Now, we solve for A(T) = 100 = 1700 e^(-T*k)
100/1700 = e^(-Tk)
ln(100/1700) = -Tk
-1/k ln(100/1700) = T, where k = -1/8 ln(1000/1700)