The present population of a town is 26010. It increases annually at the rate of 2%. What was the population of town two years ago ?

Options

A. 25000
B. 25100
C. 25200
D. 25500

Answer

To find the population of the town two years ago, given that the present population is 26,010 and it increases annually at a rate of 2%, we can use the formula for population growth. The formula to calculate the past population based on the present population and the growth rate is:

\[ P = \frac{P_0}{(1 + r)^n} \]

Where:
- \( P_0 \) = Present population
- \( r \) = Growth rate (in decimal)
- \( n \) = Number of years in the past

### Step 1: Identify the values
- Present population (\( P_0 \)) = 26,010
- Growth rate (\( r \)) = 2% = 0.02 (in decimal)
- Number of years (\( n \)) = 2

### Step 2: Substitute the values into the formula
We can substitute the values into the formula:

\[ P = \frac{26010}{(1 + 0.02)^2} \]

### Step 3: Calculate \( (1 + 0.02)^2 \)
First, calculate \( (1 + 0.02) \):

\[ 1 + 0.02 = 1.02 \]

Now, square it:

\[ (1.02)^2 = 1.0404 \]

### Step 4: Divide the present population by the squared value
Now, substitute back into the equation:

\[ P = \frac{26010}{1.0404} \]

### Step 5: Perform the division
Now, calculate the division:

\[ P \approx 25000 \]

### Conclusion
The population of the town two years ago was approximately 25,000.

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