In a proliferating cell system, the number of mitotic divisions required to produce 1024 cells from a single parent cell are _______________Correct answer is '10'. Can you explain this answer?

Question

Answer

Introduction:
In a proliferating cell system, cells undergo mitotic divisions to produce new cells. Each mitotic division results in the formation of two daughter cells. The number of mitotic divisions required to produce a certain number of cells can be determined using exponential growth.

Explanation:
To solve this problem, we can use the formula for exponential growth:

N = N0 * 2^n

Where:
N = final number of cells
N0 = initial number of cells (in this case, 1)
n = number of divisions

We need to find the value of n when N = 1024.

Step 1: Calculate the value of n:
Let's substitute the given values into the formula:

1024 = 1 * 2^n

Simplifying the equation:

2^n = 1024

Taking the logarithm of both sides:

log(2^n) = log(1024)

Using the logarithmic property:

n * log(2) = log(1024)

Simplifying further:

n = log(1024) / log(2)

Using a calculator, we can find the value of n:

n ≈ 10

Therefore, the number of mitotic divisions required to produce 1024 cells from a single parent cell is 10.

Conclusion:
In a proliferating cell system, 10 mitotic divisions are required to produce 1024 cells from a single parent cell. This can be determined using the exponential growth formula N = N0 * 2^n, where N is the final number of cells, N0 is the initial number of cells, and n is the number of divisions.

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