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 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2000?

Round your answer to the nearest integer.

To calculate the projected number of AIDS-related deaths in 2000 based on the exponential growth model, we can use the formula for exponential growth:

\[
N(t) = N_0 \cdot r^t
\]

where:
- \( N(t) \) is the population at time \( t \),
- \( N_0 \) is the initial population (1800 deaths in 1983),
- \( r \) is the growth factor (1.8),
- \( t \) is the number of time intervals (years).

1. **Determine \( t \)**: From 1983 to 2000, there are \( 2000 - 1983 = 17 \) years.
2. **Plug values into the formula**:

\[
N(17) = 1800 \cdot (1.8)^{17}
\]

Now we can calculate it:

\[
N(17) = 1800 \cdot (1.8)^{17}
\]

Calculating \( (1.8)^{17} \):

\[
(1.8)^{17} \approx 11390.65
\]

Now, multiplying by 1800:

\[
N(17) \approx 1800 \cdot 11390.65 \approx 20401200
\]

Rounding to the nearest integer, approximately **20,401,200 people** would have died from AIDS in 2000 if the trend had continued unchecked.

### Summary
Approximately **20,401,200** deaths from AIDS in 2000.

Would you like details on the calculations, or do you have any questions? Here are some related questions you might consider:

1. What factors could influence the actual spread of AIDS compared to this model?
2. How do public health interventions impact the growth factor of diseases?
3. What other diseases exhibit exponential growth patterns?
4. How can understanding exponential growth help in planning healthcare responses?
5. What are the limitations of using exponential models in predicting disease spread? 

**Tip:** Always consider the impact of external factors when applying mathematical models to real-world situations.

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 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2000?

Explore the exponential growth model applied to AIDS-related deaths, estimating that approximately 20,401,200 people would have died from AIDS in 2000 based on a growth factor of 1.8 and an initial death count of 1800 in 1983.

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