Cells undergoing mitosis double with each cycle. A biologist has a sample containing 15 cells. Which graph and equation represents the number of cells after each cycle occurs?

1. Initial Condition: 

The initial number of cells is 15. 
2. Doubling Each Cycle: 

The number of cells doubles with each cycle, which can be represented by the equation \(y = 15( 2) ^ x\), where \(x\) is the number of cycles. 
3. Graph Matching: 

The correct graph should start at 15 cells (when \(x = 0\)) and double with each cycle. 
4. Verification: 
- For \(x = 0\): \(y = 15( 2) ^ 0 = 15\) 
- For \(x = 1\): \(y = 15( 2) ^ 1 = 30\) 
- For \(x = 2\): \(y = 15( 2) ^ 2 = 60\) 
- For \(x = 3\): \(y = 15( 2) ^ 3 = 120\) 
5. Conclusion: 

The graph and equation that represent the number of cells after each cycle is X. \(y = 15( 2) ^ x\).

Supplemental Knowledge:

Mitosis is a process where a single cell divides to produce two identical daughter cells. When cells double with each cycle, this represents exponential growth. The general form of an exponential growth equation is:

\[y = a \cdot b^ x\]

where: 
- \(y\) is the final quantity, 
- \(a\) is the initial quantity, 
- \(b\) is the base (growth factor), 
- \(x\) is the number of cycles.

Given that the initial number of cells (\(a\)) is 15 and they double each cycle (\(b = 2\)), the equation representing this scenario would be:

\[y = 15 \cdot 2^ x\]

Real-Life Connections:

Knowledge of exponential growth can be essential in various fields. When studying how bacteria thrive in lab cultures, knowing their population tends to multiply exponentially can help you predict how fast things will expand under ideal circumstances.

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