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.

To solve this problem, we will use the formula for exponential growth:

\[ N(t) = N_0 \times e^{rt} \]

where:
- \( N(t) \) is the number of infected people at time \( t \),
- \( N_0 \) is the initial number of infected people,
- \( r \) is the growth rate,
- \( t \) is the time in days.

Given:
- \( N_0 = 28 \) (initial number of infected people),
- \( r = 0.045 \) (growth rate per day, converted to decimal form from 4.5%),
- \( t = 10 \) days.

We substitute these values into the formula:

\[ N(10) = 28 \times e^{0.045 \times 10} \]

First, calculate the exponent:

\[ 0.045 \times 10 = 0.45 \]

Now, compute \( e^{0.45} \):

\[ e^{0.45} \approx 1.5683 \]

Next, multiply this by the initial number of infected people:

\[ N(10) = 28 \times 1.5683 \approx 43.9124 \]

Rounding to the nearest whole number, we get:

\[ N(10) \approx 44 \]

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

Would you like more details or have any questions about this calculation?

Here are 5 additional questions you might consider:
1. How would the number of infections change if the growth rate increased to 6% per day?
2. How many days would it take for the number of infected people to double at the same growth rate?
3. What is the general formula for continuous exponential growth and how is it derived?
4. How does the concept of half-life relate to exponential decay?
5. Can you explain the difference between

Learn how to calculate the number of people infected with a disease over time using exponential growth. Example problem: If initially 28 people are infected and the disease spreads at a rate of 4.5% per day, find the number infected after 10 days. Understand the exponential growth formula and how to apply it to real-world scenarios.

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