The number of people infected with a disease is spreading at a rate of 4.5% per day. If initially 28 people are infected, find the number infected 10 days. Round to the nearest day. Please use the model A(t)=Ie^rt where r is the growth rate/decay.

To find the number of people infected after 10 days using the exponential growth model \( A(t) = I e^{rt} \), we need to follow these steps:

1. Identify the initial number of infected people \( I \).
2. Identify the growth rate \( r \).
3. Identify the time period \( t \).
4. Plug these values into the formula and solve for \( A(t) \).

Here are the given values:
- Initial number of infected people, \( I = 28 \)
- Growth rate per day, \( r = 4.5\% = 0.045 \)
- Time period, \( t = 10 \) days

The formula is:
\[ A(t) = I e^{rt} \]

Substitute the given values into the formula:
\[ A(10) = 28 e^{0.045 \cdot 10} \]

First, calculate the exponent:
\[ 0.045 \cdot 10 = 0.45 \]

Then, calculate \( e^{0.45} \):
\[ e^{0.45} \approx 1.5683 \]

Now, multiply this by the initial number of infected people:
\[ A(10) = 28 \cdot 1.5683 \approx 43.9 \]

Rounding to the nearest whole number:
\[ A(10) \approx 44 \]

So, the number of people infected after 10 days is approximately 44.

Would you like any further details or have any questions?

Here are 5 more questions you might want to ask:
1. How does changing the growth rate affect the number of infected people?
2. Can you explain the significance of the constant \( e \) in the model?
3. How would the model change if the disease spread at a decreasing rate?
4. What if the initial number of infected people was different?
5. How would you model this problem if the growth rate varied each day?

**Tip:** When dealing with exponential growth, small changes in the growth rate or initial conditions can lead to significant differences over time, so precise calculations are crucial.

Learn how to calculate the number of people infected with a disease spreading at a rate of 4.5% daily using the exponential growth model A(t) = I e^(rt). Initial 28 people infected. Find the number infected after 10 days.

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