In a forest at present, there are 176 rabbits. The population of rabbits doubles every 6 months. How many months back, there were at the most 10 rabbits in the forest ?

Options

A. 4 yr
B. 2 yr
C. 30 mon
D. 36 mon

Explanation

To solve the problem, we need to determine how many months ago there were at most 10 rabbits in the forest, given that the current population is 176 rabbits and it doubles every 6 months.

### Step-by-Step Solution:

1. **Understanding the Doubling of Population**:
The population of rabbits doubles every 6 months. This means if we go back in time, the population will halve every 6 months.

2. **Current Population**:
At present, the population is 176 rabbits.

3. **Calculating the Population Backwards**:
We will calculate the population of rabbits at intervals of 6 months going back in time until we reach a number that is at most 10.

- **0 months ago (Present)**: 176 rabbits
- **6 months ago**: \( \frac{176}{2} = 88 \) rabbits
- **12 months ago**: \( \frac{88}{2} = 44 \) rabbits
- **18 months ago**: \( \frac{44}{2} = 22 \) rabbits
- **24 months ago**: \( \frac{22}{2} = 11 \) rabbits
- **30 months ago**: \( \frac{11}{2} = 5.5 \) rabbits

4. **Rounding the Population**:
Since we cannot have a fraction of a rabbit, we round 5.5 down to 5. Thus, 30 months ago, there were approximately 5 rabbits.

5. **Determining When the Population Was At Most 10**:
The last population count that was greater than 10 was 11 rabbits (24 months ago). Therefore, the population was at most 10 rabbits starting from 30 months ago.

6. **Final Answer**:
Thus, the number of months back when there were at most 10 rabbits in the forest is **30 months**.