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When organic waste is dumped into a pond, the oxidation process that takes place reduces the pond's oxygen content. However, given time, nature will restore th...

Question

When organic waste is dumped into a pond, the oxidation process that takes place reduces the pond's oxygen content. However, given time, nature will restore the oxygen content to its natural level. Suppose the oxygen content $t$ days after organic waste has been dumped into the pond is given by $$ P=100\left(\frac{t^{2}+10 t+100}{t^{2}+20 t+100}\right) $$ percent of its normal level. Find $t$ corresponding to an oxygen content of $80 \%$ and interpret your results.

When organic waste is dumped into a pond, the oxidation process that takes place reduces the pond's oxygen content. However, given time, nature will restore the oxygen content to its natural level. Suppose the oxygen content $t$ days after organic waste has been dumped into the pond is given by $$ P=100\left(\frac{t^{2}+10 t+100}{t^{2}+20 t+100}\right) $$ percent of its normal level. Find $t$ corresponding to an oxygen content of $80 \%$ and interpret your results.



Answers

Water flows from the bottom of a storage tank at a rate of $ r(t) = 200 - 4t $ liters per minute, where $ 0 \le t \le 50 $. Find the amount of water that flows from the tank during the first 10 minutes.


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