Question

A group consisting of 30 aggressive zombies doubles in size every hour. Which equation matches the number of zombies after 8 hours?
Answer
Multiple Choice Answers
Z, equals, 2, left parenthesis, 1, plus, 30, right parenthesis, to the power 8Z=2(1+30)
8

Z, equals, 2, left parenthesis, 30, right parenthesis, to the power 8Z=2(30)
8

Z, equals, 30, left parenthesis, 2, right parenthesis, to the power 8Z=30(2)
8

Z, equals, 30, left parenthesis, 1, plus, 2, right parenthesis, to the power 8Z=30(1+2)
8

Answer 1

To determine the correct equation that matches the number of zombies after 8 hours, we start with the initial count of zombies and how they grow over time.

1. **Initial Count**: There are 30 zombies.
2. **Doubling Rate**: The number of zombies doubles every hour.
3. **Time Period**: We are looking for the count of zombies after 8 hours.

The formula to calculate the number of zombies after time \( t \) in hours, when the initial number of zombies is \( N_0 \) and the population doubles every hour, can be expressed as:

\[
Z = N_0 \times (2^t)
\]

Where:
- \( Z \) is the number of zombies after \( t \) hours.
- \( N_0 \) is the initial number of zombies (30 in this case).
- \( t \) is the number of hours (8 in this case).

Plugging in the values gives:

\[
Z = 30 \times (2^8)
\]

From the given multiple choice answers, this matches the following format:

\[
Z = 30(2^8)
\]

Thus, the correct answer from the options provided is:

\[
\boxed{Z = 30(2^8)}
\]