Using the fed-batch data in the excel spreadsheet provided, calculate (a) cell specific growth rate and doubling time, (b) cell specific glucose consumption and lactate production rates, and (c) the cell specific IgG production rates. Calculate these parameters using differential and integral methods. For (a) and (b) focus only on the exponential phase of the growth while for (c) perform the analysis for the whole culture period.

Days in Culture	Viable cell density	Viability	Nova pH	Nova Glucose (Gluc) g/L	Nova Lactate (Lac) g/L	Titer (mg/L)
0.0	1.87E+05	90.30	7.201	6.1	0	0
1.4	3.86E+05	95.20	7.042	6	0.05	18.05
2.3	6.40E+05	93.90	7.074	5.8	0.1	29.55
2.7	8.00E+05	93.80	7.064	5.5	0.3	36.65
3.3	1.15E+06	93.60	6.916	5.2	0.5	58.5
3.9	1.73E+06	93.60	6.639	4.75	0.8	65
4.5	2.40E+06	88.80	6.688	4.1	1.1	70.5
5.0	3.76E+06	92.40	6.698	3.1	1.8	135.5
5.7	4.94E+06	93.20	6.683	2	2.8	189.5
6.2	6.70E+06	92.10	6.666	0.5	3.89	250.5
6.9	8.09E+06	91.60	6.692	0	4.1	368.5
7.4	8.86E+06	88.70	6.743	0	4.05	495
8.1	1.02E+07	87.70	6.73	0	4	641.5
8.6	1.17E+07	87.00	6.75	0	3.8	767.6
9.5	1.23E+07	84.60	6.885	0	3.76	962.5
9.9	1.24E+07	81.80	6.81	0	3.7	1148
10.6	1.35E+07	79.10	6.851	0	3.44	1366
11.1	1.31E+07	76.10	6.851	0	3.4	1575
11.8	1.27E+07	72.70	6.964	0	3.2	1756
12.3	1.17E+07	63.70	6.919	0	3.4	1962
12.9	9.84E+06	59.20	6.961	0	3.2	2112
13.4	8.87E+06	47.90	6.985	0	3.12	2215
14.1	7.15E+06	40.80	7.044	0	3	2328