Question

In 2003, the population of a district was 27,600. With a continuous annual growth rate of approximately 3%, what will the population be in 2018 according to the exponential growth function?

Answer 1

To calculate the population in 2018 using the exponential growth function, we need to follow these steps:

1. Start with the initial population in 2003, which is 27,600.
2. Determine the annual growth rate, which is approximately 3%. Convert this percentage to a decimal by dividing it by 100: 3% = 0.03.

3. Use the exponential growth formula: P(t) = P(0) * e^(r * t), where P(t) represents the population at time t, P(0) is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time period in years.
4. Calculate the population in 2018, which is 15 years after 2003 (2018 - 2003 = 15). Substitute the values into the formula: P(15) = 27,600 * e^(0.03 * 15).

Using a calculator, we can find that e^(0.03 * 15) is approximately 1.513.
Therefore, P(15) ≈ 27,600 * 1.513 = 41,721.8. Round this value to the nearest whole number to get the estimated population in 2018: 41,722.

So according to the exponential growth function, the population in the district is estimated to be around 41,722 in 2018.