Viruses can be highly contagious and sometimes deadly, such as the Ebola virus. A similar virus has emerged and nothing is known about its transmission, but similar to Ebola, this virus has an infection rate of 75% every week. Since there are no vaccines available and modern medical facilities are showing to be ineffective at stopping the spread, it is considered uncontained and will grow exponentially. When discovered, 100 people are affected by the virus.How many people will be infected by the end of week 8? Round to the nearest whole person.

To calculate the number of people infected by the end of week 8, we can use the formula for exponential growth:

\[
N = N_0 \times (1 + r)^t
\]

Where:
- \(N\) is the final number of people infected.
- \(N_0\) is the initial number of infected people (100).
- \(r\) is the infection rate (75% or 0.75).
- \(t\) is the time in weeks (8).

Plugging in the values:

\[
N = 100 \times (1 + 0.75)^8
\]
\[
N = 100 \times (1.75)^8
\]

Calculating \( (1.75)^8 \):

\[
(1.75)^8 \approx 41.15
\]

Now calculating \(N\):

\[
N \approx 100 \times 41.15 \approx 4115
\]

Rounding to the nearest whole person, approximately **4,115 people** will be infected by the end of week 8.

Would you like more details or do you have any questions? Here are some related questions you might consider:

1. How does the infection rate affect the spread of other viruses?
2. What measures can be taken to contain a virus with such a high infection rate?
3. How do exponential growth patterns apply in real-world scenarios?
4. What historical examples exist of similar viral outbreaks?
5. What role do public health policies play in managing outbreaks? 

**Tip:** Understanding the basic principles of exponential growth can help you analyze similar situations in epidemiology.

How many people will be infected by the end of week 8 if a virus has an infection rate of 75% every week and starts with 100 people infected?

Discover how to calculate the exponential growth of a virus infection starting with 100 people and an infection rate of 75% per week, resulting in approximately 4,115 infections by the end of week 8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation