To find the number of zombies after 2 hours, given that a group of 23 aggressive zombies quadruples in size every hour, we need to understand the process step by step.
1. Initial Count: The initial number of zombies is 23.
2. Growth Factor: The zombies quadruple in size every hour. This means that each hour, the number of zombies gets multiplied by 4.
3. Time Period: We need to find the number of zombies after 2 hours.
Let’s break down the growth over the 2 hours.
First Hour:
- Initial = 23
- After 1 hour = 23 4
Second Hour:
- The number of zombies after 1 hour will be 23 4.
- After 2 hours = (23 4) 4
We can simplify this by combining the multiplication:
- After 2 hours = 23 (4 4)
Let's rewrite this:
- After 2 hours = 23 * 4^2
Thus, the equation that represents the number of zombies after 2 hours is:
[tex]\[ Z = 23 \times 4^2 \][/tex]
Now, evaluating each of the given options:
1. [tex]\(Z=23(4)(4)(4)(4)\)[/tex]
- This implies multiplying 23 by 4 four times, which is incorrect since we only quadruple twice (once for each hour).
2. [tex]\(Z=4(23)^2\)[/tex]
- This suggests squaring the initial number of zombies (which doesn’t align with the growth rate of quadrupling).
3. [tex]\(Z=4(1+23)^2\)[/tex]
- This expression simplifies to 4 times the square of 24, which also doesn’t align with our quadrupling growth model.
4. [tex]\(Z=23(4)^2\)[/tex]
- This correctly represents quadrupling the zombie count over 2 hours.
Therefore, the correct answer is:
[tex]\[ Z = 23 \times 4^2 \][/tex]
Given this equation, the number of zombies after 2 hours is indeed 368.
