3. Find when the population of Atlanta, GA will be 600,000

To estimate when the population of Atlanta, Georgia, will reach 600,000, we'll use available data and apply a basic population growth model. ### **Current Population and Growth Rate** - **Recent Population Data:** As of the **2020 U.S. Census**, the population of Atlanta city proper was approximately **498,715**. - **Estimated Growth Rate:** Historically, Atlanta has experienced an annual population growth rate of about **1% to 2%**. For this estimation, we'll consider both scenarios. ### **Population Growth Calculation** We'll use the **compound annual growth formula**: \[ P(t) = P_0 \times (1 + r)^t \] where: - \( P(t) \) = Future population - \( P_0 \) = Current population (498,715) - \( r \) = Annual growth rate (as a decimal) - \( t \) = Number of years We want to find \( t \) when \( P(t) = 600,000 \). #### **1. At a 1% Annual Growth Rate** \[ 600,000 = 498,715 \times (1 + 0.01)^t \] \[ \frac{600,000}{498,715} = (1.01)^t \] \[ 1.203 = (1.01)^t \] Taking the natural logarithm on both sides: \[ \ln(1.203) = t \times \ln(1.01) \] \[ t = \frac{\ln(1.203)}{\ln(1.01)} \approx \frac{0.184}{0.00995} \approx 18.5 \text{ years} \] **Estimated Year:** **2020 + 18.5 ≈ 2038** #### **2. At a 2% Annual Growth Rate** \[ 600,000 = 498,715 \times (1 + 0.02)^t \] \[ \frac{600,000}{498,715} = (1.02)^t \] \[ 1.203 = (1.02)^t \] Taking the natural logarithm on both sides: \[ \ln(1.203) = t \times \ln(1.02) \] \[ t = \frac{\ln(1.203)}{\ln(1.02)} \approx \frac{0.184}{0.0198} \approx 9.3 \text{ years} \] **Estimated Year:** **2020 + 9.3 ≈ 2029** ### **Conclusion** Based on these calculations: - **At a 1% annual growth rate**, Atlanta's population is projected to reach **600,000 around the year 2038**. - **At a 2% annual growth rate**, this milestone could be achieved by **around 2029**. **Realistic Expectation:** Considering urban growth trends and factors that may influence migration, economic opportunities, and birth rates, a **balanced estimate** would place Atlanta reaching a population of **600,000 between 2030 and 2040**. **Please Note:** These projections are based on historical growth rates and assume that current trends continue. Factors such as economic changes, housing developments, policy decisions, and unforeseen events (like pandemics) can significantly impact population growth rates.