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 1500 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2007?

   ? people

(Note: once diseases become widespread, they start to behave more like logistic growth, but don't worry about that for the purpose of this exercise)

To solve this problem, we'll use the exponential growth model formula:

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

where:
- \(P(t)\) is the population at time \(t\),
- \(P_0\) is the initial population,
- \(r\) is the growth factor (common ratio),
- \(t\) is the time in years since the start.

Given:
- Initial population in 1983, \(P_0 = 1500\),
- Growth factor, \(r = 1.8\),
- We want to find the population in 2007, so the time elapsed \(t = 2007 - 1983 = 24\) years.

Substitute these values into the formula:

\[
P(24) = 1500 \times 1.8^{24}
\]

Now let's calculate this step-by-step:

1. Calculate \(1.8^{24}\).

2. Multiply the result by 1500.

Let's calculate the value:

\[
P(24) = 1500 \times 1.8^{24}
\]If the trend had continued unchecked, approximately **2,007,388,268** people would have died from AIDS in the U.S. by 2007 according to the exponential growth model.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What are other examples of phenomena that follow an exponential growth model?
2. How does the exponential growth model differ from the logistic growth model?
3. What factors might cause the growth rate of a disease to slow down over time?
4. How can public health interventions impact the growth rate of a disease?
5. What mathematical models can be used to predict the spread of a disease in a population?

**Tip:** Exponential growth can lead to very large numbers quickly. It's important to consider real-world factors that may limit growth, such as resource availability or intervention measures.

Learn how to predict the number of AIDS deaths in the U.S. by 2007 using the exponential growth model. Starting with 1500 deaths in 1983 and a growth factor of 1.8, calculate the projected deaths by 2007. Step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation