Based on the information provided regarding the data and the behavior of strain B zombies, we can analyze the options for the exponential growth of the zombie population.
Given that:
- Strain B zombies can infect 1 person every minute.
This points toward an exponential growth model of the form \( y = a \cdot b^x \) where:
- \( a \) is the initial quantity,
- \( b \) is the growth factor,
- \( x \) is the time in minutes.
For a model of infection:
- Each infected zombie can infect 1 new person every minute, which suggests that the number of newly infected individuals doubles as each infected zombie continues to infect more individuals. Therefore, the growth factor is likely to be 2.
Based on this reasoning, the most appropriate equation from your given options would be:
Answer: \( y = 2^x \)
This indicates that the number of zombies (or infections) grows exponentially as time passes, specifically doubling every minute.
Graphing the Equation: To graph the equation \( y = 2^x \):
- The x-axis represents time (in minutes),
- The y-axis represents the number of zombies.
You'll see that at \( x = 0 \), \( y = 1 \) (initial infected), at \( x = 1 \), \( y = 2 \), at \( x = 2 \), \( y = 4 \), at \( x = 3 \), \( y = 8 \), and so forth.
The graph will show rapid growth, characteristic of an exponential function. If you are in a graphing tool, you can plot it across a suitable range, such as \( x = 0 \) to \( x = 10 \).
Please note that I can't create a live graph here, but you can easily plot this using graphing software or online tools by entering the equation \( y = 2^x \).
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