1. **State the problem:** We want to find how many people would have died from AIDS in 2003 if the number of deaths grew exponentially from 1600 in 1983 with a growth factor of 2.2 per year. 2. **Formula used:** The exponential growth model is given by $$N(t) = N_0 \times r^{t - t_0}$$ where: - $N(t)$ is the number of deaths at year $t$, - $N_0$ is the initial number of deaths at year $t_0$, - $r$ is the growth factor (common ratio), - $t - t_0$ is the number of years elapsed. 3. **Given values:** - $N_0 = 1600$ (deaths in 1983), - $r = 2.2$, - $t_0 = 1983$, - $t = 2003$. 4. **Calculate the number of years elapsed:** $$t - t_0 = 2003 - 1983 = 20$$ 5. **Apply the formula:** $$N(2003) = 1600 \times 2.2^{20}$$ 6. **Calculate $2.2^{20}$:** Using a calculator, $2.2^{20} \approx 383375.999$. 7. **Multiply by initial deaths:** $$N(2003) = 1600 \times 383375.999 = 613401598.4$$ 8. **Interpretation:** If the exponential growth had continued unchecked, about 613,401,598 people would have died from AIDS in 2003. **Final answer:** $$\boxed{613401598}$$