In 2008 there were 70 million people worldwide who had been infected with a particular disease. At that time the infection rate was 4.7 million people per year.
​(a) Write a formula for a linear function that models the total number of people in millions who were infected with the particular disease x years after 2008.
​(b) Estimate the number of people who may have been infected by the year 2013.

We can solve the problem in two parts, as requested:

### Part (a): Write a formula for a linear function

In 2008, there were 70 million people infected, and the infection rate was increasing by 4.7 million people per year. This scenario can be modeled by a linear function.

Let:
- \( P(x) \) represent the total number of infected people (in millions) \( x \) years after 2008.
- \( x \) represent the number of years after 2008.

The linear function can be written in the slope-intercept form:  
\[
P(x) = mx + b
\]
Where:
- \( m \) is the rate of change (slope), which is 4.7 million people per year.
- \( b \) is the initial value in 2008, which is 70 million.

Thus, the formula for the linear function is:
\[
P(x) = 4.7x + 70
\]

### Part (b): Estimate the number of people infected by 2013

To estimate the number of people infected by 2013, we first calculate the value of \( x \). Since 2013 is 5 years after 2008:
\[
x = 2013 - 2008 = 5
\]
Now, substitute \( x = 5 \) into the linear function:
\[
P(5) = 4.7(5) + 70 = 23.5 + 70 = 93.5
\]
Thus, the estimated number of people infected by the year 2013 is **93.5 million**.

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Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the model change if the infection rate increased by 10% every year?
2. What would be the infection count in 2020 using this model?
3. How would the graph of this function look over a 20-year span?
4. How does the slope \( m = 4.7 \) affect the prediction for future years?
5. Can you express the infection rate as a percentage of the population per year?

**Tip:** In linear models, the slope represents the rate of change, giving us key insights into how quickly the situation evolves over time.

In 2008 there were 70 million people worldwide who had been infected with a particular disease. At that time the infection rate was 4.7 million people per year. (a) Write a formula for a linear function that models the total number of people in millions who were infected with the particular disease x years after 2008. (b) Estimate the number of people who may have been infected by the year 2013.

Explore how to model disease spread using a linear function. In this example, 70 million people were infected in 2008, with an infection rate of 4.7 million people per year. Learn how to write the formula and estimate infections by 2013. Suitable for Grades 8-10.

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