M144 Assignment

On June 1^st, a fast-growing algae is introduced into Fish Lake. It starts to grow and cover the surface of the lake in such a way that the area covered by the algae doubles every day. If the algae growth is left unchecked, the algae will cover the entire surface of Fish Lake on June 16^th and all the fish in Fish Lake will suffocate.

a.       a) When will the lake be covered half-way?

a.       b) Assume nobody tries to clean up the algae. Write an equation that represents the percentage of the surface area of the lake that is covered in algae as a function of time (in days) that passes since the algae was introduced into the lake. (Consider June 1^st to be day zero, so June 16^th would be day 15).

a.       c) While jogging by the lake on June 12^th, a biologist notices the presence of the algae and recognizes what type of algae it is. Alarmed the biologist tells the mayor of Cheney about the problem. The mayor assures the biologist that he saw the algae as well that she shouldn’t be alarmed. Why would the mayor not consider the algae a serious problem at this point? (Use numbers to support your answer).

a.       d) A cleanup crew is brought in on June 15^th to Fish Lake and removes 99% of the algae. How effective will this solution be?

a.       e) On what day of the month will one fifth of the lake be covered in algae?