SOLUTION: An endangered species of fish has a population that is decreasing exponentially (A = aekt). The population 9 years ago was 1700. Today, only 1000 of the fish are alive. Once the p

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Question 926974: An endangered species of fish has a population that is decreasing exponentially (A = aekt). The population 9
years ago was 1700. Today, only 1000 of the fish are alive. Once the population drops below 100, the situation
will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let 9 years ago be t=0, then,
1700=ae%5E%28k%280%29%29=a
So today, t=9
1000=1700e%5E%28k%289%29%29
e%5E%289k%29=10%2F17
9k=ln%2810%2F17%29
k=%281%2F9%29ln%2810%2F17%29
So find t so that,
1700e%5E%28kt%29=100
e%5E%28kt%29=1%2F17
kt=ln%281%2F17%29
t=ln%281%2F17%29%2F%28%281%2F9%29ln%2810%2F17%29%29
t=9%28ln%281%29-ln%2817%29%29%2F%28ln%2810%29-ln%2817%29%29
highlight%28t=9%28ln%2817%29%29%2F%28ln%2817%29-ln%2810%29%29%29