The population of a city is 200,000. If the annual birth rate and the annual death rate are 6% and 3% respectively, then calculate the population of the city after 2 years.

Options

A. 212090
B. 206090
C. `212,000`
D. 212180

Answer

To calculate the population of the city after 2 years given the annual birth rate and death rate, we can follow these steps:

### Step 1: Understand the Initial Population
The initial population of the city is given as 200,000.

### Step 2: Calculate the Net Growth Rate
The net growth rate can be calculated by subtracting the death rate from the birth rate:
- Birth rate = 6% = 0.06
- Death rate = 3% = 0.03
- Net growth rate = Birth rate - Death rate = 0.06 - 0.03 = 0.03 or 3%

### Step 3: Calculate the Population After 1 Year
To find the population after 1 year, we can use the formula:
\[ \text{Population after 1 year} = \text{Initial Population} \times (1 + \text{Net Growth Rate}) \]
Substituting the values:
\[ \text{Population after 1 year} = 200,000 \times (1 + 0.03) \]
\[ \text{Population after 1 year} = 200,000 \times 1.03 = 206,000 \]

### Step 4: Calculate the Population After 2 Years
Now, we will use the population after 1 year to calculate the population after the second year:
\[ \text{Population after 2 years} = \text{Population after 1 year} \times (1 + \text{Net Growth Rate}) \]
Substituting the values:
\[ \text{Population after 2 years} = 206,000 \times (1 + 0.03) \]
\[ \text{Population after 2 years} = 206,000 \times 1.03 = 212,180 \]

### Final Answer
The population of the city after 2 years will be approximately **212,180**.

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