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 predict the population in 2015 based on the given data from 2005, we can follow these steps:

### Step 1: Identify the Initial Population
The initial population in 2005 is given as 14 million.

### Step 2: Calculate the Rate of Natural Increase (r)
The rate of natural increase (r) can be calculated using the formula:
\[ r = \text{birth rate} - \text{death rate} \]
Given:
- Birth rate = 0.028
- Death rate = 0.008

Calculating r:
\[ r = 0.028 - 0.008 = 0.020 \]

### Step 3: Use the Exponential Growth Formula
The exponential growth formula is:
\[ \frac{dn}{dt} = r \cdot n \]
Where:
- \( \frac{dn}{dt} \) is the change in population over time,
- \( r \) is the rate of natural increase,
- \( n \) is the initial population.

### Step 4: Calculate the Change in Population Over 10 Years
Now we can calculate the change in population over 10 years (from 2005 to 2015):
\[ \frac{dn}{dt} = r \cdot n \]
Substituting the values:
\[ \frac{dn}{dt} = 0.020 \cdot 14,000,000 \]

Calculating:
\[ \frac{dn}{dt} = 280,000 \]

### Step 5: Calculate the New Population
To find the population in 2015, we add the change in population to the initial population:
\[ \text{Population in 2015} = \text{Initial Population} + \frac{dn}{dt} \]
\[ \text{Population in 2015} = 14,000,000 + 280,000 \]
\[ \text{Population in 2015} = 14,280,000 \]

### Step 6: Round the Population
For simplicity, we can round the population:
\[ \text{Population in 2015} \approx 14.3 \text{ million} \]

### Final Answer
The predicted population in 2015 is approximately **14.3 million**.

---