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A group consisting of 21 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 4 hours?

Z=21(3)^(4)

Z=3(21)^(4)

Z=3(21)(21)(21)(21)

Z=21(3)(3)

A group consisting of 2121 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 44 hours?\newlineZ=21(3)4 Z=21(3)^{4} \newlineZ=3(21)4 Z=3(21)^{4} \newlineZ=3(21)(21)(21)(21) Z=3(21)(21)(21)(21) \newlineZ=21(3)(3) Z=21(3)(3)

Full solution

Q. A group consisting of 2121 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 44 hours?\newlineZ=21(3)4 Z=21(3)^{4} \newlineZ=3(21)4 Z=3(21)^{4} \newlineZ=3(21)(21)(21)(21) Z=3(21)(21)(21)(21) \newlineZ=21(3)(3) Z=21(3)(3)
  1. Calculate Growth Rate: We need to find the number of zombies after 44 hours, given that the initial number of zombies is 2121 and the population triples every hour. The formula to calculate the number of zombies after a certain number of hours when the population is tripling every hour is:\newlineZ=initial number of zombies×(growth rate)number of hoursZ = \text{initial number of zombies} \times (\text{growth rate})^{\text{number of hours}}\newlineIn this case, the initial number of zombies is 2121, the growth rate is 33 (since the population triples), and the number of hours is 44.\newlineSo the equation that matches the number of zombies after 44 hours is:\newlineZ=21×(3)4Z = 21 \times (3)^4
  2. Calculate Exponential Value: Now we calculate the value of 33 raised to the power of 44. \newline34=3×3×3×33^4 = 3 \times 3 \times 3 \times 3\newline34=813^4 = 81
  3. Find Total Zombies: Next, we multiply the initial number of zombies, 2121, by 8181 to find the total number of zombies after 44 hours.\newlineZ=21×81Z = 21 \times 81\newlineZ=1701Z = 1701

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