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To solve this problem, we can use the formula for exponential growth:

\[
P(t) = P_0 \cdot r^t
\]

Where:
- \( P(t) \) is the population (or number of deaths) at time \( t \),
- \( P_0 \) is the initial population (number of deaths in 1983),
- \( r \) is the growth rate (2.1 in this case),
- \( t \) is the time elapsed since the initial year (in years).

### Step 1: Identify the values
- \( P_0 = 2000 \) (number of deaths in 1983),
- \( r = 2.1 \) (growth factor),
- The time difference from 1983 to 2005 is \( t = 2005 - 1983 = 22 \) years.

### Step 2: Apply the formula
\[
P(22) = 2000 \cdot (2.1)^{22}
\]

### Step 3: Calculate
Let me compute this for you.After calculating, if the trend had continued unchecked, approximately **24,538,865,477** people would have died from AIDS in 2005, which is clearly unrealistic due to population limitations. This highlights why, in reality, growth models like exponential growth don't apply indefinitely for diseases, as mentioned in the note.

Would you like to explore more about this growth model or clarify any part of the solution?

Here are five related questions you might find interesting:
1. What are the key differences between exponential and logistic growth?
2. How does the growth rate affect the outcome in exponential models?
3. What happens when the growth factor is less than 1 in an exponential model?
4. How can we adjust models to account for limiting factors in real populations?
5. In what other real-world scenarios is exponential growth applicable?

**Tip:** Always check if exponential growth assumptions are reasonable for long periods, as real-world factors often prevent infinite growth.

Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.1. In 1983, about 2000 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005?

Learn how to use the exponential growth model to estimate the number of AIDS-related deaths in the U.S. from 1983 to 2005, using a growth factor of 2.1 and initial deaths of 2000 in 1983. A detailed step-by-step solution is provided for high school-level students.

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