Question

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

(I'm not sure if you're still supposed to add a 1 if the rate is a whole number like 4..)

A) Z = 4(1+5)^8

B) Z = 5(4)^8

C) Z = 5(1+4)^8

D) Z = 5(4)

Answer 1

B) Z = 5(4)^8

Explanation:

To determine the equation that matches the number of zombies after 8 hours, let's analyze the given information.

The initial group consists of 5 aggressive zombies, and their size quadruples every hour. This means that for each hour that passes, the number of zombies becomes four times larger.

After 1 hour: 5 zombies * 4 = 20 zombies

After 2 hours: 20 zombies * 4 = 80 zombies

After 3 hours: 80 zombies * 4 = 320 zombies

After 4 hours: 320 zombies * 4 = 1280 zombies

After 5 hours: 1280 zombies * 4 = 5120 zombies

After 6 hours: 5120 zombies * 4 = 20480 zombies

After 7 hours: 20480 zombies * 4 = 81920 zombies

After 8 hours: 81920 zombies * 4 = 327680 zombies

By observing the pattern, we can see that the number of zombies is multiplying by 4 every hour.

Among the given options, the equation that matches the number of zombies after 8 hours is:

B) Z = 5(4)^8

Using this equation, when we substitute 8 for the exponent, we get:

Z = 5(4^8) = 5(65536) = 327680

Therefore, the number of zombies after 8 hours is 327680.