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.

(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 = C0ekt; power-law growth, C = ktb. 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?