Given information:
- The experiment starts with 10 bacterial cells.
- After the nth generation, the number of cells becomes 105.

To find:
- The value of n (the number of generations).

Approach:
- We can use the exponential growth formula to solve this problem.
- The formula for exponential growth is given by: N = N0 * (1+r)^n, where N is the final number of cells, N0 is the initial number of cells, r is the growth rate, and n is the number of generations.

Solution:
1. Let's assume the growth rate (r) for the bacterial cells is constant.
2. From the given information, we know that the initial number of cells (N0) is 10 and the final number of cells (N) is 105.
3. Substituting these values into the exponential growth formula, we get: 105 = 10 * (1+r)^n.
4. We need to find the value of n, so we can rearrange the equation as follows: (1+r)^n = 105/10.
5. Simplifying the right side of the equation, we get: (1+r)^n = 10.5.
6. Taking the logarithm of both sides of the equation, we have: n * log(1+r) = log(10.5).
7. Dividing both sides of the equation by log(1+r), we get: n = log(10.5) / log(1+r).

Calculating the value of n:
1. Using a scientific calculator, we can find that log(10.5) ≈ 1.02119.
2. To find the value of log(1+r), we can use trial and error.
3. By trying different values of r, we can find that log(1+0.02) ≈ 0.0198 and log(1+0.03) ≈ 0.0296.
4. Substituting these values into the equation, we get: n = 1.02119 / 0.0198 ≈ 51.59 and n = 1.02119 / 0.0296 ≈ 34.54.
5. Since we are looking for a whole number value for n, we can conclude that the value lies between 34 and 52.
6. The correct answer, as mentioned in the question, is between 13.26 and 13.30, which is not within the range we calculated.
7. Therefore, there might be some additional information or constraints missing in the question, as the given answer is not consistent with the calculations.