Final answer:
To calculate the number of cells after binary fission, use the equation Nn = No2^n, where No is the initial number of cells and n is the number of generations. If No = 4 and we have 3 generations, this results in 32 cells.
Step-by-step explanation:
Calculating the Number of Cells after Binary Fission
To calculate the number of cells (Nt) that replicate by binary fission, we use the equation Nn = No2^n. Here, No is the initial number of cells, n is the number of generations, and Nn refers to the number of cells after n generations. For example, if we start with No = 4 cells, and the generation time is 30 minutes, in 90 minutes we would have passed through 3 generations (j = 3). Using the formula, we find N3 = 4 × 2^3, which equals 4 × 8 or 32 cells.
Bacterial cells often divide by binary fission and follow a growth pattern through lag, logarithmic, stationary, and death phases. In a controlled environment, if we know the generation time and starting cell count, we can predict the cell population at any future time as it grows exponentially.
For precise calculations, rounding numbers must be done correctly, keeping in mind rules such as rounding up if the next digit is larger than 5.