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5. A new species of algae grows in a lake at a rate given by N(t) = 4s, where N is the number of algae

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5. A new species of algae grows in a lake at a rate given by N(t) = 4s, where N is the number of algae cells and t is the time in days, form when the new species was first introduced to the lake. Researchers notice that the algae is taking over the lake really quickly and introduce a chemical to put into the lake to kill the algae cells. The chemical is put into the lake 25 days after the first algae cell made its way into the lake. The number of cells killed is given by K(t) = 3ez, where K is the number of algae cells killed after t days. Determine the maximum number of algae cells that were present in the lake and determine the time at which this occurred.

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