2.34. 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 3850 cells, and at 5 p.m. the cell count has reached 36,530.
- 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 = Co + kt; exponential growth, C = Coe*'; power-law growth, C = ktb. In these expressions, Co is the initial cell concentration and k and b arc constants.
- Select the most reasonable of the three formulas and justify your selection.
- Estimate the initial number of cells present at 8 a.m. (/ = 0). State any assumptions you make.
- 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?
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