The population of a town increas es by 5% every year. If the present population is 9261, the population 3 years ago was

Options

A. 8000
B. 5700
C. 6000
D. 7500

Answer

To find the population of the town 3 years ago, we need to reverse the effect of the 5% annual increase over the past 3 years.

### Step-by-Step Solution:

1. **Identify the present population**:
The present population is given as 9261.

2. **Understand the annual increase**:
The population increases by 5% each year. This means that if the population was P last year, this year it is P + 0.05P = 1.05P.

3. **Calculate the population 3 years ago**:
To find the population 3 years ago, we need to reverse the increase for 3 years. We can use the formula for reversing percentage increase:
\[ \text{Population 3 years ago} = \frac{\text{Present Population}}{(1 + \text{Rate})^n} \]
where Rate = 5% = 0.05 and n = 3 years.

4. **Substitute the values into the formula**:
\[ \text{Population 3 years ago} = \frac{9261}{(1 + 0.05)^3} \]
\[ = \frac{9261}{(1.05)^3} \]

5. **Calculate \( (1.05)^3 \)**:
\[ (1.05)^3 = 1.157625 \]

6. **Now divide the present population by this value**:
\[ \text{Population 3 years ago} = \frac{9261}{1.157625} \approx 8000 \]

7. **Conclusion**:
The population of the town 3 years ago was approximately 8000.