Question

Starting with a single cell, what will be number of cells after 'n' cycles of cell division, given that in each cycle every cell divides into two cells?

• A. \(2^2\)
• B. \(n^n\)
• C. \(n^2\)
• D. \(2^n\)

Hint:

For questions involving exponential growth due to repeated doubling, use the formula \(2^n\), where \(n\) is the number of divisions.

Answer 1

The Correct Option is D

Step 1: Understand the cell division process
Each cycle of cell division causes every cell present to divide into two daughter cells.

Step 2: Analyze how the number of cells increases
Start with 1 cell.
After 1st cycle: \(2^1 = 2\) cells.
After 2nd cycle: \(2^2 = 4\) cells.
After 3rd cycle: \(2^3 = 8\) cells.
After \(n\) cycles: the total number of cells becomes \(2^n\).

Step 3: Eliminate incorrect options
\(2^2\) is correct only for \(n = 2\), not general.
\(n^n\) and \(n^2\) do not represent exponential growth.
Therefore, only \(2^n\) correctly models exponential cell division.