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Let's analyze the problem using the given table of "Growth Rate of Rapidly Dividing Human Liver Cell" to solve the questions about mitosis.

From the table, the number of cells doubles every 10 hours:

- Time = 0 hours: 1 cell
- Time = 10 hours: 2 cells
- Time = 20 hours: 4 cells
- Time = 30 hours: 8 cells
- Time = 40 hours: 16 cells
- Time = 50 hours: 32 cells

### (a) How many cells will there be in one week, assuming no cells die?

We observe a doubling pattern every 10 hours. To calculate the number of cells in one week (168 hours), we can use the formula for exponential growth:

\[
N(t) = N_0 \times 2^{\frac{t}{10}}
\]

Where:
- \(N(t)\) is the number of cells at time \(t\),
- \(N_0\) is the initial number of cells (1 at \(t = 0\)),
- \(t\) is the time in hours, and
- The exponent \(\frac{t}{10}\) represents the number of doubling periods.

For one week (168 hours):

\[
N(168) = 1 \times 2^{\frac{168}{10}} = 2^{16.8}
\]

Calculating \(2^{16.8}\), we get approximately:

\[
N(168) \approx 101,559
\]

So, there will be around **101,559 cells** in one week.

### (b) How many copies of each chromosome will there be in 60 hours, assuming the original cell is diploid and divides mitotically?

Mitosis produces two identical daughter cells, each with the same number of chromosomes as the parent. If the original cell is diploid, it maintains this number of chromosomes during each division. Since the number of cells doubles every 10 hours, in 60 hours, the cells will double 6 times.

Using the same formula for exponential growth:

\[
N(60) = 1 \times 2^{\frac{60}{10}} = 2^6 = 64
\]

There will be 64 cells after 60 hours. Since each cell has the same diploid number of chromosomes, there will be **64 copies of each chromosome** in total.

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Do you need more details or have any questions?

Here are some related questions:
1. How would the result change if cells doubled every 8 hours instead of 10?
2. What if a portion of the cells died every 24 hours—how would that affect the population?
3. Can this model be used for other types of cells or only liver cells?
4. What is the significance of the diploid state during mitosis in this context?
5. How would the growth change if the cells entered a dormant phase after a certain time?

**Tip:** Exponential growth models like this are common in biology but often reach a limit when resources are depleted or space becomes a constraint.

Assuming no cells die, how many cells will there be in one week? Assuming the original cell is diploid and divides mitotically, how many copies of each chromosome will there be in 60 hours?

Understand how to calculate the growth of human liver cells using an exponential growth model. Learn to apply cell division concepts to determine the number of cells in one week and chromosome copies after 60 hours. Suitable for high school students studying biology and exponential growth.

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