Complete The Table To Show The Total Number Of Cells After 5 Hours.$\[ \begin{tabular}{|c|c|c|c|} \hline Hour & Expression & Power & Number Of Cells \\ \hline 1 & 2 & $2^1$ & 2 \\ \hline 2 & $2 \cdot 2$ & $2^2$ & 4 \\ \hline 3 & $2 \cdot 2 \cdot 2$

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The given table provides information about the number of cells present at different hours, along with the expression and power associated with each hour. The table is as follows:

Hour Expression Power Number of Cells
1 2 212^1 2
2 2⋅22 \cdot 2 222^2 4
3 2⋅2⋅22 \cdot 2 \cdot 2 232^3 8

Calculating the Number of Cells at Each Hour

To calculate the total number of cells after 5 hours, we need to understand the pattern in the number of cells at each hour. Looking at the table, we can see that the number of cells at each hour is twice the number of cells at the previous hour.

Hour Expression Power Number of Cells
1 2 212^1 2
2 2⋅22 \cdot 2 222^2 4
3 2⋅2⋅22 \cdot 2 \cdot 2 232^3 8
4 2⋅2⋅2⋅22 \cdot 2 \cdot 2 \cdot 2 242^4 16
5 2⋅2⋅2⋅2⋅22 \cdot 2 \cdot 2 \cdot 2 \cdot 2 252^5 32

Calculating the Total Number of Cells After 5 Hours

Now that we have the number of cells at each hour, we can calculate the total number of cells after 5 hours by adding the number of cells at each hour.

Total number of cells after 5 hours = 2 + 4 + 8 + 16 + 32 Total number of cells after 5 hours = 62

Conclusion

In this problem, we were given a table with information about the number of cells present at different hours, along with the expression and power associated with each hour. We calculated the number of cells at each hour and then added them to find the total number of cells after 5 hours.

Step-by-Step Solution

  1. Understand the pattern in the number of cells at each hour.
  2. Calculate the number of cells at each hour using the pattern.
  3. Add the number of cells at each hour to find the total number of cells after 5 hours.

Key Concepts

  • Pattern recognition
  • Exponential growth
  • Addition of numbers

Real-World Applications

This problem can be applied to real-world scenarios where exponential growth is observed, such as population growth, financial growth, or any other situation where the number of cells or units grows exponentially.

Tips and Tricks

  • Always look for patterns in the given data.
  • Use the pattern to calculate the number of cells at each hour.
  • Add the number of cells at each hour to find the total number of cells after 5 hours.

Common Mistakes

  • Not recognizing the pattern in the number of cells at each hour.
  • Not using the pattern to calculate the number of cells at each hour.
  • Not adding the number of cells at each hour to find the total number of cells after 5 hours.

Conclusion

Q: What is the pattern in the number of cells at each hour?

A: The pattern in the number of cells at each hour is that the number of cells at each hour is twice the number of cells at the previous hour.

Q: How do we calculate the number of cells at each hour?

A: We calculate the number of cells at each hour by using the pattern. For example, at hour 1, the number of cells is 2. At hour 2, the number of cells is 2 x 2 = 4. At hour 3, the number of cells is 2 x 2 x 2 = 8, and so on.

Q: How do we add the number of cells at each hour to find the total number of cells after 5 hours?

A: We add the number of cells at each hour by simply adding the numbers together. For example, the total number of cells after 5 hours is 2 + 4 + 8 + 16 + 32 = 62.

Q: What is the total number of cells after 5 hours?

A: The total number of cells after 5 hours is 62.

Q: Can we apply this concept to real-world scenarios?

A: Yes, this concept can be applied to real-world scenarios where exponential growth is observed, such as population growth, financial growth, or any other situation where the number of cells or units grows exponentially.

Q: What are some common mistakes to avoid when calculating the total number of cells after 5 hours?

A: Some common mistakes to avoid when calculating the total number of cells after 5 hours include:

  • Not recognizing the pattern in the number of cells at each hour.
  • Not using the pattern to calculate the number of cells at each hour.
  • Not adding the number of cells at each hour to find the total number of cells after 5 hours.

Q: How can we use this concept to solve other problems?

A: We can use this concept to solve other problems by recognizing the pattern in the number of cells at each hour and using it to calculate the total number of cells after a certain number of hours.

Q: What are some tips and tricks for solving this type of problem?

A: Some tips and tricks for solving this type of problem include:

  • Always look for patterns in the given data.
  • Use the pattern to calculate the number of cells at each hour.
  • Add the number of cells at each hour to find the total number of cells after a certain number of hours.

Q: What are some key concepts that are important to understand when solving this type of problem?

A: Some key concepts that are important to understand when solving this type of problem include:

  • Pattern recognition
  • Exponential growth
  • Addition of numbers

Q: Can we use this concept to solve problems with different types of growth?

A: Yes, we can use this concept to solve problems with different types of growth, such as linear growth or quadratic growth.

Q: How can we apply this concept to real-world scenarios?

A: We can apply this concept to real-world scenarios by recognizing the type of growth that is occurring and using the appropriate formula to calculate the total number of cells or units after a certain number of hours.

Q: What are some examples of real-world scenarios where this concept can be applied?

A: Some examples of real-world scenarios where this concept can be applied include:

  • Population growth
  • Financial growth
  • Exponential growth in any field where the number of cells or units grows exponentially.