1. **State the problem:** We want to find the predicted area of the Amazon rainforest 100 years after the end of a 50-year period, given it decreased by 20% over those 50 years and the area at the end of that period is 3,290,125 km². 2. **Understand the decay model:** The rainforest area decreases by 20% over 50 years, so the remaining area is 80% of the original. This is an exponential decay problem. 3. **Formula for exponential decay:** $$ A = A_0 \times (1 - r)^t $$ where $A$ is the area after time $t$, $A_0$ is the initial area, $r$ is the decay rate per time period, and $t$ is the number of time periods. 4. **Identify values:** - Decay rate $r = 0.20$ over 50 years - Area at end of 50 years $A = 3,290,125$ km² - We want area after $t = 100$ years from that point 5. **Find the decay factor per 50 years:** $$ 1 - r = 0.80 $$ 6. **Calculate the decay factor per year:** $$ (0.80)^{\frac{1}{50}} $$ 7. **Calculate the decay factor for 100 years:** $$ (0.80)^{\frac{100}{50}} = (0.80)^2 = 0.64 $$ 8. **Calculate predicted area after 100 years from the end of the 50-year period:** $$ A_{100} = 3,290,125 \times 0.64 = 2,105,680 $$ **Final answer:** The predicted area of the Amazon rainforest 100 years later is approximately **2,105,680 km²**.