Based on the information provided about Strain B, the relationship can be described as an exponential growth model due to the multiplicative effect of each zombie being able to infect one new person every minute.
Analysis of Strain B:
- Initial Condition: Let’s assume patient zero (the first zombie) starts the infection. Therefore, at time \(t = 0\), there is 1 zombie.
- Infection Rate: Every minute, each zombie infects one new person.
This means the number of zombies doubles every minute:
- At \(t = 0\) minutes, there is 1 zombie.
- At \(t = 1\) minute, there are 2 zombies (1 original + 1 new).
- At \(t = 2\) minutes, there are 4 zombies (2 original + 2 new).
- At \(t = 3\) minutes, there are 8 zombies (4 original + 4 new).
Graph Type:
The appropriate graph for Strain B would be an exponential growth graph whereby the x-axis represents time in minutes, and the y-axis represents the number of zombies.
Equation:
To formulate this mathematically, you can use the equation: \[ N(t) = N_0 \cdot 2^t \] Where:
- \(N(t)\) is the number of zombies at time \(t\).
- \(N_0\) is the initial number of zombies (which is 1 in this case).
- \(t\) is time in minutes.
Plugging in the initial value: \[ N(t) = 1 \cdot 2^t \] which simplifies to: \[ N(t) = 2^t \]
Conclusion:
Thus, the number of zombies after each minute can be represented by the equation \( N(t) = 2^t \), indicating that the number of zombies doubles every minute, characteristic of an exponential growth pattern.
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