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

Options

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

Answer

To find the population of the town 2 years ago given the current population and the annual growth rate, we can use the formula for population growth:

\[ P = P_0 (1 + r)^t \]

Where:
- \( P \) is the present population,
- \( P_0 \) is the population at time \( t \) years ago,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the number of years.

Given:
- Present population \( P = 26010 \)
- Growth rate \( r = 2\% = \frac{2}{100} = 0.02 \)
- Time \( t = 2 \) years

We need to find \( P_0 \).

### Step 1: Rearranging the formula
We can rearrange the formula to solve for \( P_0 \):

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

### Step 2: Substitute the values into the formula
Now we substitute the known values into the formula:

\[ P_0 = \frac{26010}{(1 + 0.02)^2} \]

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

\[ (1 + 0.02)^2 = 1.02^2 = 1.0404 \]

### Step 4: Calculate \( P_0 \)
Now substitute this back into the equation for \( P_0 \):

\[ P_0 = \frac{26010}{1.0404} \]

### Step 5: Perform the division
Now we perform the division:

\[ P_0 \approx 25000 \]

### Conclusion
The population of the town 2 years ago was approximately **25,000**.

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