In 2005, for each of the 14 million people present in a country, `0.028` were born and `0.008` died during the year. Using exponential equation, the number of people present in 2015 is predicted as

Options

A. 25 millions
B. 17 millions
C. 20 millions
D. 18 millions

Explanation

To solve the problem of predicting the population in 2015 based on the given birth and death rates, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Population (N)**:
- The initial population in 2005 is given as 14 million.
- \( N = 14,000,000 \)

2. **Determine Birth Rate and Death Rate**:
- Birth rate (b) = 0.028 (per capita per year)
- Death rate (d) = 0.008 (per capita per year)

3. **Calculate the Intrinsic Rate of Natural Increase (r)**:
- The intrinsic rate of natural increase (r) is calculated by subtracting the death rate from the birth rate:
\[ r = b - d = 0.028 - 0.008 = 0.02 \]

4. **Calculate the Growth Rate per Year**:
- The growth rate (G) for the entire population can be calculated using the formula:
\[ G = r \times N \]
- Substituting the values:
\[ G = 0.02 \times 14,000,000 = 280,000 \]
- This means the population increases by 280,000 individuals per year.

5. **Calculate the Total Increase Over 10 Years**:
- Since we are looking for the population after 10 years (from 2005 to 2015), we multiply the annual growth by 10:
\[ \text{Total Increase} = G \times 10 = 280,000 \times 10 = 2,800,000 \]

6. **Calculate the Predicted Population in 2015**:
- Finally, we add the total increase to the initial population to find the predicted population in 2015:
\[ \text{Predicted Population} = N + \text{Total Increase} = 14,000,000 + 2,800,000 = 16,800,000 \]

7. **Round the Population**:
- The final population can be rounded to the nearest million:
\[ \text{Predicted Population} \approx 17,000,000 \]

### Final Answer:
The predicted population in 2015 is approximately **17 million**.

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