When organic matter is introduced into a body of water, the oxygen content of the water is temporarily reduced by oxidation. Suppose that t days after untreated sewage is dumped into a particular lake, the proportion of the usual oxygen content in the water of the lake that remains is given by the function

a. At what rate is the oxygen proportion P(t) changing after 10 days? Is the proportion increasing or decreasing at this time?

b. Is the oxygen proportion increasing or decreasing after 15 days?

c. If there is no new dumping, what would you expect to eventually happen to the proportion of oxygen? Use a limit to verify your conjecture.

Transcribed Image Text:

P(t) = 1 12 t + 12 + 144 (t + 12)²