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A group consisting of 8 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 5 hours?

Z=3(1+8)^(5)

Z=3(8)^(5)

Z=8(3)^(5)

Z=8(3)

A group consisting of $8$ aggressive zombies triples in size every hour. Which equation matches the number of zombies after $5$ hours? $\newline$ $Z=3(1+8)^{5}$ $\newline$ $Z=3(8)^{5}$ $\newline$ $Z=8(3)^{5}$ $\newline$ $Z=8(3)$

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Write exponential functions: word problems

Full solution

Q. A group consisting of

8

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

5

hours?

\newline

Z=3(1+8)^{5}

\newline

Z=3(8)^{5}

\newline

Z=8(3)^{5}

\newline

Z=8(3)

Define Variables: Let's define the variables for the equation: $\newline$ - Let $Z$ be the number of zombies after a certain number of hours. $\newline$ - The initial number of zombies is $8$ . $\newline$ - The growth rate is a tripling every hour, which means the growth factor is $3$ .
Exponential Growth Equation: We need to find the equation that models the exponential growth of the zombie population. The general form of an exponential growth equation is $Z = a(b)^t$ , where: $\newline$ - $a$ is the initial amount, $\newline$ - $b$ is the growth factor, $\newline$ - $t$ is the time in hours.
Substitute Values: Since the initial number of zombies is $8$ and the growth factor is $3$ (because the group triples in size every hour), we can substitute these values into the equation to get $Z = 8(3)^t$ .
Calculate After $5$ Hours: We want to find the number of zombies after $5$ hours, so we will substitute $t$ with $5$ in the equation $Z = 8(3)^t$ to get $Z = 8(3)^5$ .
Calculate Value: Now we calculate the value of $Z$ after $5$ hours using the equation $Z = 8(3)^5$ . This means we need to raise $3$ to the power of $5$ and then multiply the result by $8$ . $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$ $Z = 8 \times 243$
Total Number of Zombies: Multiplying $8$ by $243$ gives us the total number of zombies after $5$ hours. $\newline$ $Z = 8 \times 243 = 1944$

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