A rabbit population doubles every month. If the population of rabbits is 32 at the end of the first month, how many rabbits will there be after eight months?(2 points) The initial number of rabbits is . The common ratio is . The number of rabbits after eight months is .

Answer 1

To solve this problem, we start with the information given:

1. The population doubles every month.
2. The population at the end of the first month is 32 rabbits.

From this, we can determine the following:

• Initial number of rabbits: The population at the start (which we will call \( P_0 \)) can be calculated by realizing that it doubles to 32 at the end of the first month. Thus:

  \[ P_0 = \frac{32}{2} = 16 \]

• Common ratio: The common ratio (\( r \)) in this case is 2, because the population doubles each month.

• Population after eight months: The formula to find the population after \( n \) months where the population doubles is given by:

  \[ P_n = P_0 \times r^n \]

  Here, \( n = 8 \), \( P_0 = 16 \), and \( r = 2 \). Plugging in these values:

  \[ P_8 = 16 \times 2^8 \]

  First, we calculate \( 2^8 \):

  \[ 2^8 = 256 \]

  Now we can find \( P_8 \):

  \[ P_8 = 16 \times 256 = 4096 \]

Putting it all together, we have:

• The initial number of rabbits is 16.
• The common ratio is 2.
• The number of rabbits after eight months is 4096.

Thus the final answer is:

• The initial number of rabbits is 16.
• The common ratio is 2.
• The number of rabbits after eight months is 4096.