1. An apple grower finds that if she plants 20 trees per acre, each tree will yield 90 bushels of apples. She also estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acres to maximize her harvest?
2. Epidemiologists have found a new communicable disease running rampant in College Station, Texas. They estimate that t days after the disease is first observed in the community, the percent of the population infected by the disease is approximated by p(t) = (20t3 - t4)/1000 for 0 ≤ t ≤ 20. After how many days is the percent of the population infected a maximum? What is the maximum percent of the population infected?
3. A lake polluted by bacteria is treated with an antibacterial chemical. After t days, the number N of bacteria per milliliter of water is approximated by N(t) = 20((t/12) - ln(t/12)) + 30 for 1 ≤ t ≤ 15. When during this time will the number of bacteria be a minimum? What is the minimum number of bacteria during this time? When during this time will the number of bacteria be at a maximum?
4. The reproduction function for the Antarctic blue whale is estimated to be f(p) = -0.0004p2 + 1.06p, where p and f(p) are in thousands. Find the population that gives the maximum sustainable yield, and the size of the yield.
5. The reproduction function for king salmon in the Bering Sea is f(p) = -(1/8)p2 + 7.5p, where p and f(p) are in thousand metric tons. Find the population that gives the maximum sustainable yield, and the size of the yield.