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 . Remaining Attempts : 3

Answer 1

To solve the rabbit population problem, we can break it down step by step.

1. Identify the initial number of rabbits: Given that the population is 32 at the end of the first month, we can deduce that the initial population at the beginning (0 months) is half of that, which is: \[ \text{Initial population} = \frac{32}{2} = 16 \]

2. Determine the common ratio: The population doubles each month, which means the common ratio for this exponential growth is: \[ \text{Common ratio} = 2 \]

3. Determine the population after eight months: Since the population doubles each month, we can express the population after \( n \) months with the formula: \[ P(n) = P(0) \times r^n \] where \( P(0) \) is the initial population, \( r \) is the common ratio, and \( n \) is the number of months.

   Plugging in the values: \[ P(8) = 16 \times 2^8 \]

   Now, calculate \( 2^8 \): \[ 2^8 = 256 \]

   So, the population after eight months will be: \[ P(8) = 16 \times 256 = 4096 \]

Finally, we can summarize the answers:

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