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A cell divides to form two new cells every 24 hours.How many days will it take for the original cell to divide into 8 cells?

Question

A cell divides to form two new cells every 24 hours.

How many days will it take for the original cell to divide into 8 cells?

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Solution

1. Break Down the Problem

To solve how many days it will take for one cell to divide into 8 cells, we need to identify how the cell divides over time. Each division results in the formation of two cells. This is a scenario involving exponential growth.

2. Relevant Concepts

The growth of cells can be represented as:

  • After 1 division (24 hours), 1 cell → 2 cells
  • After 2 divisions (48 hours), 2 cells → 4 cells
  • After 3 divisions (72 hours), 4 cells → 8 cells

This shows that after every 24 hours, the number of cells doubles.

3. Analysis and Detail

We want to find the number of divisions required to reach 8 cells starting with 1 cell:

  • 12 1 \to 2 (after 1 day)
  • 24 2 \to 4 (after 2 days)
  • 48 4 \to 8 (after 3 days)

From this we can conclude that:

  • The original cell doubles after each day, so to reach 8, we need 3 days.

4. Verify and Summarize

The total time taken for a single cell to become 8 cells is 3 days, as verified by counting the number of divisions and the corresponding time intervals.

Final Answer

It will take 3 days for the original cell to divide into 8 cells.

This problem has been solved

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