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 1: Identify the initial population and rates
- The initial population (N) in 2005 is 14 million.
- The birth rate (b) is 0.028.
- The death rate (d) is 0.008.

### Step 2: Calculate the net growth rate (r)
- The net growth rate (r) is calculated by subtracting the death rate from the birth rate:
\[ r = b - d = 0.028 - 0.008 = 0.020 \]

### Step 3: Use the exponential growth formula
- The formula for exponential growth is given by:
\[ N(t) = N_0 \cdot e^{rt} \]
where:
- \( N(t) \) is the population at time \( t \),
- \( N_0 \) is the initial population,
- \( r \) is the net growth rate,
- \( t \) is the time in years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

### Step 4: Calculate the time period
- The time period from 2005 to 2015 is 10 years (t = 10).

### Step 5: Substitute the values into the formula
- Substituting the values into the formula:
\[ N(10) = 14 \cdot e^{0.020 \cdot 10} \]
\[ N(10) = 14 \cdot e^{0.20} \]

### Step 6: Calculate \( e^{0.20} \)
- Using a calculator, we find that \( e^{0.20} \) is approximately 1.2214.

### Step 7: Calculate the predicted population
- Now, substituting this value back into the equation:
\[ N(10) = 14 \cdot 1.2214 \approx 17.1 \text{ million} \]

### Step 8: Round to the nearest million
- Rounding 17.1 million gives us approximately 17 million.

### Conclusion
- Therefore, the predicted population in 2015 is approximately **17 million**.