Question

A lake was closed because of an accidental pesticide spill. The concentration of the pesticide after the spill was 848 parts per million. Each day the water is tested, and the amount of pesticide is found to be about 75% of what was there the day before. Do you think the lake will ever be completely free of the pesticide? Explain.

Answer 1

Explanation:

`a_(n)=a_(1)r^(n-1)\\0=848(0.75)^(n-1)\\or~(0.75)^(n-1)=0\\0.75<1\\so~(0.75)^(n-1) \rightarrow 0,if~n-1 \rightarrow ~\infty`

`or~n \rightarrow 1+\infty\\or~n \rightarrow \infty`

Hence lake will never be free of pesticide.