You arrive at your lab at 8 A. M. and add an indeterminate quantity of bacterial cells to a flask. At 11 A. M you measure the number of cells using a spectrophotometer (the absorbance of light is directly related to the number of cells) and determine from a previous calibration that the flask contains 4550 cells/mL, and at 5 P. M. the cell concentration has reached 48530 cells/mL. A. Fit each of the following formulas to the two given data points (that is, determine the values of the two constants in each formula): linear growth, C = C0 + kt; exponential growth, C = C0e^kt; power-law growth, C = kt^b. In these expressions, C0 is the initial cell concentration and k and b are constants.
B. Select the most reasonable of the three formulas and justify your selection.
C. Estimate the initial number of cells present at 8 A. M. (t = 0). State any assumptions you make. D. The culture needs to be split into two equal parts once the number of cells reaches 2 million. Estimate the time at which you would have to come back to perform this task. State any assumptions you make. If this is a routine operation that you must perform often, what does your result suggest about the scheduling of the experiment?