Otis monitors the number of strep infections reported in a certain neighborhood each week. According to his reports, infections are growing at a rate of 28% per week.

If the number of infections starts at 8 and continues to grow exponentially, what will the number of infections be in week 7?

38 infections

26 infections

45 infections

31 infections

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

\[
P(t) = P_0 \times (1 + r)^t
\]

where:
- \(P(t)\) is the population (number of infections) at time \(t\),
- \(P_0\) is the initial population (number of infections),
- \(r\) is the growth rate (as a decimal),
- \(t\) is the number of time periods (weeks, in this case).

Given:
- Initial number of infections, \(P_0 = 8\),
- Growth rate, \(r = 28\% = 0.28\),
- Time period, \(t = 7\) weeks.

Now, let's calculate the number of infections at week 7.

\[
P(7) = 8 \times (1 + 0.28)^7
\]

I'll calculate that.The number of infections at week 7 will be approximately 45. Therefore, the correct answer is **45 infections**.

Do you want more details or have any questions?

Here are some related questions:

1. How would the number of infections change if the growth rate were 20% instead of 28%?
2. What would be the number of infections at week 5?
3. How does exponential growth compare to linear growth over time?
4. How long will it take for the infections to double at this growth rate?
5. What is the weekly infection rate if the initial number of infections was 10 instead of 8?
6. How does the growth rate affect the total number of infections in the long run?
7. Can you model the situation where the growth rate decreases by 2% each week?
8. What would be the infection count after 10 weeks?

**Tip:** In exponential growth problems, small changes in the growth rate can lead to significant differences in the outcome over time.

Explore how to calculate exponential growth of infections starting at 8 with a 28% weekly increase, reaching approximately 45 infections by week 7. Learn the formula and step-by-step solution with practical examples.

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