Question

a group consisting of 23 aggressive zombies quadruples in size every hour. which equation matches the number of zombies after 2 hours?
answer
\\( z = 23(4)(4)(4)(4) \\)
\\( z = 4(23)^2 \\)
\\( z = 4(1 + 23)^2 \\)
\\( z = 23(4)^2 \\)

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth where quantity quadruples each hour is $Z = P(4)^t$, where $P$ is initial population, $t$ is time in hours.

Step2: Identify given values

Initial population $P=23$, time $t=2$ hours.

Step3: Substitute values into formula

Substitute $P=23$ and $t=2$ into the growth formula: $Z = 23(4)^2$

Step4: Eliminate incorrect options

• $Z = 23(4)(4)(4)(4)$ uses $t=4$, wrong time.
• $Z = 4(23)^2$ swaps initial value and growth factor.
• $Z = 4(1+23)^2$ uses incorrect growth structure.

Answer:

$Z = 23(4)^2$