A group consisting of $23$ aggressive zombies triples in size every hour. Which equation matches the number of zombies after $2$ hours? $\newline$ $Z=23(3)^{2}$ $\newline$ $Z=3(1+23)^{2}$ $\newline$ $Z=23(1+3)^{2}$ $\newline$ $Z=3(23)(23)$

Full solution

Q. A group consisting of

23

aggressive zombies triples in size every hour. Which equation matches the number of zombies after

2

hours?

\newline

Z=23(3)^{2}

\newline

Z=3(1+23)^{2}

\newline

Z=23(1+3)^{2}

\newline

Z=3(23)(23)

Understand the problem: Understand the problem. $\newline$ We need to find the equation that correctly represents the number of zombies after $2$ hours, given that the initial number of zombies is $23$ and the population triples every hour.
Determine base number and rate: Determine the base number of zombies and the rate of growth. $\newline$ The base number of zombies is $23$ , and the rate of growth is tripling every hour, which is a multiplication by $3$ .
Apply exponential growth formula: Apply the exponential growth formula. $\newline$ The general formula for exponential growth is $\text{Initial Population} \times \text{Growth Rate}^{\text{Time Period}}$ . In this case, the Initial Population is $23$ , the Growth Rate is $3$ , and the Time Period is $2$ hours.
Plug values into formula: Plug the values into the formula to get the equation. $\newline$ $Z = 23 \times 3^{2}$
Evaluate options: Evaluate the options given in the problem to see which one matches our equation. $\newline$ Option A: $Z = 23(3)^{2}$ matches our equation from Step $4$ . $\newline$ Option B: $Z = 3(1+23)^{2}$ does not match because it suggests adding $1$ to $23$ before raising to the power of $2$ . $\newline$ Option C: $Z = 23(1+3)^{2}$ does not match because it suggests adding $1$ to $3$ before squaring, which is not the correct growth rate. $\newline$ Option D: $Z = 3(23)(23)$ does not match because it suggests multiplying $23$ by itself, which is not the correct growth pattern.