Answer:
Step-by-step explanation:
To calculate the population of the city in a future year, you can use the formula for exponential growth:
\[P(t) = P_0 \cdot e^{rt}\]
Where:
- \(P(t)\) is the population at time \(t\).
- \(P_0\) is the initial population (5.68 million in 2012).
- \(r\) is the annual growth rate (2.79% or 0.0279 as a decimal).
- \(t\) is the number of years in the future.
Let's say you want to calculate the population in the year 2022 (10 years into the future). Plug these values into the formula:
\[P(10) = 5.68 \, \text{million} \cdot e^{0.0279 \cdot 10}\]
Now, calculate it:
\[P(10) = 5.68 \, \text{million} \cdot e^{0.279}\]
Using a calculator or a computer, you can calculate the value of \(e^{0.279}\), which is approximately 1.322. Now, multiply:
\[P(10) = 5.68 \, \text{million} \cdot 1.322\]
\[P(10) \approx 7.515 \, \text{million}\]
So, the estimated population of the city in the year 2022 is approximately 7.515 million.