SOLUTION: An endangered species of fish has a population that is decreasing exponentially. The population 7 years ago was 1900. Today, only 900 of the fish are alive. Once the population dro

Algebra ->  Exponents -> SOLUTION: An endangered species of fish has a population that is decreasing exponentially. The population 7 years ago was 1900. Today, only 900 of the fish are alive. Once the population dro      Log On


   

Question 1104542: An endangered species of fish has a population that is decreasing exponentially. The population 7 years ago was 1900. Today, only 900 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 josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y=1900b%5Ex

7 years ago, time 0

1900b%5E0=1900, understood from given

1900b%5E7=900
b%5E7=9%2F19
log%28%28b%5E7%29%29=log%28%289%29%29-log%28%2819%29%29
7%2Alog%28%28b%29%29=log%28%289%29%29-log%28%2819%29%29
log%28%28b%29%29=%28log%28%289%29%29-log%28%2819%29%29%29%2F7
.
.
b=0.8988

The model for population y is highlight_green%28y=1900%280.8988%29%5Ex%29.

A BETTER model would be now today, time is 0. Choose then the 900 fish present NOW.
highlight_green%28highlight_green%28y=900%280.8988%29%5Ex%29%29 and x is years from today.
You just need to finish...