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This problem was given to me by Professor Boyd Collier from his research in Ecology. The study examines the oxygen consumption of the bug Triatoma phyllosoma after ingestion of a blood meal. In this experiment the bug matures through its fifth instar stage of development and begins its molt into the adult phase. This is a bug that causes major problems throughout South America. It spreads the deadly disease chagas when it obtains a blood meal at night from its sleeping victims. The poor rural houses may be so infested with thousands of these bugs that some of the occupants become anemic by losing up to 500 ml of blood per month.

a. Below are the data for the time, t (in hours), and the oxygen consumption, y (in ml of O₂/hr).

t	y
1	116.6
2	120.1
3	114.9
4	129.9
5	116.5
6	107.7
7	99.0
8	104.0
9	100.7
10	87.5
11	82.7
12	53.8
13	54.0
14	72.4
15	81.1

These data are most reasonably fit by a cubic equation. Follow the techniques you have used before to let Excel find the best fit to the data using the equation:

y = a₀ + a₁t + a₂t² + a₃t³.

Have trendline show the equation of the best cubic polynomial through these data. Show the plot of the data points and the best cubic polynomial through the data for t in the interval [0,15].

b. Differentiate the polynomial that you found in Part a., then determine where the derivative is zero. What is the correspondence of these numbers to the maximum and minimum values of oxygen consumption for t in the given interval? State where the function is increasing and where it is decreasing. Find any inflection points

c. Recall that at t = 0, the bug has just finished eating a blood meal, and at t = 15, it molts to become an adult. With this information briefly present a biological explanation for why you see the regions of increasing oxygen consumption and decreasing oxygen consumption. (Hint: You might want to think about your own physiology after eating a meal. The molting stage could be related to you deciding to exercise at some time after your meal.)