Three days after a Cruise ship leaves port 21 people have the flu.  Ten days after leaving the port the number infected has risen to 77.
Find the rate at which the flu is spreading per day as a decimal rounded to four decimal places

To find the rate at which the flu is spreading per day, we need to use the given data points to determine the rate of change. Let's denote the number of people infected by the flu by \( I(t) \), where \( t \) is the time in days since the cruise ship left port.

We have the following data points:
- \( I(3) = 21 \)
- \( I(10) = 77 \)

The rate at which the flu is spreading can be found by calculating the slope of the line connecting these two points. The slope (rate of change) is given by the formula:

\[
\text{slope} = \frac{I(t_2) - I(t_1)}{t_2 - t_1}
\]

Substituting the given values:

\[
\text{slope} = \frac{I(10) - I(3)}{10 - 3} = \frac{77 - 21}{10 - 3} = \frac{56}{7} = 8
\]

Therefore, the rate at which the flu is spreading per day is:

\[
\text{Rate} = 8 \text{ people per day}
\]

As a decimal rounded to four decimal places, this is:

\[
8.0000
\]

So, the rate at which the flu is spreading per day is \( 8.0000 \) people per day.

Would you like any details or have any questions about this problem?

Here are 5 more questions you might be interested in:
1. How do you find the slope of a line between two points in the coordinate plane?
2. What is the significance of the slope in a linear relationship?
3. How do you interpret the rate of change in a real-world context?
4. How can you calculate the average rate of change over a given interval?
5. How does understanding rates of change help in predicting future outcomes?

**Tip:** Always double-check your calculations for accuracy, especially when dealing with real-world data and interpretations.

Learn how to calculate the rate at which the flu is spreading per day using real-world data. Solve the problem step-by-step with the slope formula. Suitable for high school students.

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