Question

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

Answer 1

To solve the problem, let's break it down step by step.

1. **Initial Population**: We are given that the population of rabbits is 32 at the end of the first month. Since the population doubles every month, we can find the initial population (at the start of the first month) by dividing by 2:
\[
\text{Initial population} = 32 / 2 = 16
\]

2. **Common Ratio**: The common ratio here is the factor by which the population increases each month. Since the population doubles, the common ratio is:
\[
\text{Common ratio} = 2
\]

3. **Population After Eight Months**: We need to find the population after eight months. Since the population doubles each month, we can use the formula for exponential growth:
\[
\text{Population after } n \text{ months} = \text{Initial population} \times (\text{Common ratio})^n
\]
Here, \( n = 8 \):
\[
\text{Population after 8 months} = 16 \times 2^8
\]
First, calculate \( 2^8 \):
\[
2^8 = 256
\]
Now, calculate the population:
\[
\text{Population after 8 months} = 16 \times 256 = 4096
\]

Putting it all together:
- The initial number of rabbits is **16**.
- The common ratio is **2**.
- The number of rabbits after eight months is **4096**.