SOLUTION: An endangered species of fish has a population that is decreasing exponentially (( https://angel.spcollege.edu/AngelUploads/QuestionData/1f54ae24-bb77-465a-9c07-cd62ee907845/311265

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Question 688333: An endangered species of fish has a population that is decreasing exponentially (( https://angel.spcollege.edu/AngelUploads/QuestionData/1f54ae24-bb77-465a-9c07-cd62ee907845/31126544631625414447.jpg )) The population 8 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.)
I rounded and got 34 years from today....
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm getting t = 35 since I got t = 34.71486756 and rounded to the nearest integer.


A = Ao*e^(k*t)

1700 = 1000*e^(k*(-8))

1700/1000 = e^(k*(-8))

1.7 = e^(k*(-8))

-8k = ln(1.7)

k = ln(1.7)/(-8)

k = -0.0663285

-------------------------------------------

A = Ao*e^(k*t)

A = 1000*e^(-0.0663285*t)

100 = 1000*e^(-0.0663285*t)

100/1000 = e^(-0.0663285*t)

0.1 = e^(-0.0663285*t)

-0.0663285t = ln(0.1)

t = ln(0.1)/(-0.0663285)

t = 34.71486756

So it will take 35 years