1. Edsall collected through experiments the data given in the following table of the length and...

    

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1. Edsall collected through experiments the data given in the following table of the length and weight gains over 55 days of juvenile lake whitefish for various temperatures. Temp (C) Length at start Length at end Weight at start Weight at end (mm) (mm) (g) (g) 5.0 89.6 101.1 4.78 7.52 10.1 88.5 115.7 4.54 12.07 15.0 91.7 132.8 5.19 21.14 18.1 92.0 136.9 5.20 24.16 21.0 91.8 132.4 5.12 21.03 24.1 93.9 105.0 5.40 9.95 a. Find the average rate of change of length with respect to days for each of the temperature given. Give units and interpret your answer. What is happening as a general trend? b. Find the average rate of change of weight with respect to days for each of the temperatures given. Give units and interpret your answer. What is happening as a general trend? 2. Jobbagy and colleagues determined a mathematical model given by the equation G(T)=278-7.17-1.172, where G is the start of the growing season in the Patagonian steppe in Julian days (day 1-January 1) and 7 is the mean July temperature in degrees Celsius. Find the instantaneous rate of change of the day of the start of the growing season with respect to the mean July temperature and give units for (a) T = -3 (b) 7=0 3. Atwood and Helmers studied the effect of nitrogen fertilizer on corn yields in Nebraska. Nitrate contamination of groundwater in Nebraska has been a serious problem and actions such as nitrogen rationing and taxation were considered. Nitrogen fertilizer is needed to increase yields, but an excess of nitrogen does not help. Atwood and Helmers created a mathematical model given approximately by the equation Y(N)=59+0.8N-0.003N2, where N is the amount of fertilizer in pounds per acre and Y is the yield in bushels per acre. Find the instantaneous rate of change of yield with respect to the amount of fertilizer for any N on the given interval. Give units. 1. Edsall collected through experiments the data given in the following table of the length and weight gains over 55 days of juvenile lake whitefish for various temperatures. Temp (C) Length at start Length at end Weight at start Weight at end (mm) (mm) (g) (g) 5.0 89.6 101.1 4.78 7.52 10.1 88.5 115.7 4.54 12.07 15.0 91.7 132.8 5.19 21.14 18.1 92.0 136.9 5.20 24.16 21.0 91.8 132.4 5.12 21.03 24.1 93.9 105.0 5.40 9.95 a. Find the average rate of change of length with respect to days for each of the temperature given. Give units and interpret your answer. What is happening as a general trend? b. Find the average rate of change of weight with respect to days for each of the temperatures given. Give units and interpret your answer. What is happening as a general trend? 2. Jobbagy and colleagues determined a mathematical model given by the equation G(T)=278-7.17-1.172, where G is the start of the growing season in the Patagonian steppe in Julian days (day 1-January 1) and 7 is the mean July temperature in degrees Celsius. Find the instantaneous rate of change of the day of the start of the growing season with respect to the mean July temperature and give units for (a) T = -3 (b) 7=0 3. Atwood and Helmers studied the effect of nitrogen fertilizer on corn yields in Nebraska. Nitrate contamination of groundwater in Nebraska has been a serious problem and actions such as nitrogen rationing and taxation were considered. Nitrogen fertilizer is needed to increase yields, but an excess of nitrogen does not help. Atwood and Helmers created a mathematical model given approximately by the equation Y(N)=59+0.8N-0.003N2, where N is the amount of fertilizer in pounds per acre and Y is the yield in bushels per acre. Find the instantaneous rate of change of yield with respect to the amount of fertilizer for any N on the given interval. Give units.