3. With the death of Sonny Bono, there has been renewed interest in the Salton Sea. The Salton Sea formed from 1905-1907 when an engineering mistake plus heavy rains on the watershed of the then undammed Colorado River combined to break through a levee. The lake was originally freshwater but became saltier than seawater as there is no outlet and a lot of evaporation. The water going into it is fairly salty (leached from the agricultural soils). The creatures in it are mostly marine, some introduced on purpose and some accidentally with the establishment of a sport fishery. If it weren't for the agricultural and municipal wastewater flowing into the Sea it would have dried up long ago. However this water also has a lot of fertilizers, which cause massive algal blooms and a large biomass of invertebrates and fish. People like to fish there because it is so easy to catch fish, but there are also large fish kills, which are NOT pleasing. There are many birds at the Sea (there's lots of food for them), but they also experience large die-offs at times.

There are not very many kinds of metazoan zooplankton (6) in the Salton Sea, but often there is a high density present. Dr. Debbie Dexter is currently studying marine invertebrates in the Salton Sea, and a presentation of some of her work can be found on the second floor of the Life Sciences building. Mary Ann Tiffany provided me with the background information above and the data below on some of the zooplankton.

The table below lists the number/liter of various zooplankton for data averaged over depth for station S-1 (in the center of the north basin of the Salton Sea at a depth of 14 meters). The first column lists the number of days after January 1, 1997 when the data were taken. The second column represents the rotifer, Brachionus rotundiformis , the third column represents the nauplius form of the barnacle ( Balanus amphitrite ) larvae, and the last column is the nauplius form of the copepod, Apocyclops dengizicus .

a. Graph each of these species in Excel using a logarithmic scale for the population. (Create 3 separate graphs.) Determine the season of the year when each of these species is most productive.

b. Take the natural logarithm of the data for Rotifers and Barnacles, then plot these against time. Use Excel's trendline to find the best 4^th order polynomial through the logarithm of the data versus time. When Excel gives you the equation of this 4^th order polynomial, click on the formula and transform the coefficients using scientific notation with 2 decimal places.

c. Differentiate the polynomials found in Part b. and determine where the derivatives are zero. These should correspond to the three minima or maxima. Find when these minima and maxima occur and state the populations at these extrema. (Recall you have the logarithm of the populations, so you will need to exponentiate your answer.) Give the approximate dates of the minimum and the maximum that occur in the range of the data based on the polynomial fit that you found. (One should lie outside the range of the data.) Note that a maximum would be a good time for birds to feed at the Salton Sea.