SOLUTION: Help plz!! After a pollutant is dumped into a lake, each year the amount of pollutant is reduced by 18%. Considering the function A(t)=Ao(0.82)^t, the lake will be safe to swim

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Question 811253: Help plz!!
After a pollutant is dumped into a lake, each year the amount of pollutant is reduced by 18%. Considering the function A(t)=Ao(0.82)^t, the lake will be safe to swim in when the pollutant is reduced to 0.1Ao. After how many years will the lake be safe?

Answer by josgarithmetic(39632) About Me  (Show Source):
You can put this solution on YOUR website!
Find t when 0.1Ao=Ao%280.82%29%5Et
'
0.1=%280.82%29%5Et
log%2810%2C0.1%29=log%2810%2C%280.82%5Et%29%29
-1=t%2Alog%2810%2C0.82%29

t=%28-1%29%2F%28log%2810%2C0.82%29%29

t=%281%2F0.0862%29

highlight%28t=11.6%29 years