1. During the start of the COVID-19 pandemic, it is assumed that the coronavirus's spread rate is 8% daily following a simple logistic growth model. There are 350 persons assumed to have acquired the virus in province X. Assuming province X with a population of 350,000 does not follow any necessary protocol to prevent the spread of the virus, approximately how many are expected to have acquired the virus after 6 months?. Round off you answer to whole number.

To solve this problem, we use the logistic growth model, which describes how a population grows over time in an environment with a limited carrying capacity. The logistic growth formula is:

\[
P(t) = \frac{K}{1 + \left( \frac{K - P_0}{P_0} \right) e^{-rt}}
\]

where:
- \(P(t)\) is the population at time \(t\).
- \(K\) is the carrying capacity (the maximum population the environment can support), which in this case is 350,000 (the total population of province X).
- \(P_0\) is the initial population, which is 350 people.
- \(r\) is the growth rate per unit of time, which is 8% or 0.08 per day.
- \(t\) is the time in days.

### Step 1: Convert Time to Days
Since we want to calculate the number of infected people after 6 months, we first need to convert months to days. Assuming an average month has about 30 days:

\[
t = 6 \times 30 = 180 \, \text{days}
\]

### Step 2: Apply the Logistic Growth Formula
Now, we will substitute the given values into the logistic growth formula:

\[
P(180) = \frac{350000}{1 + \left( \frac{350000 - 350}{350} \right) e^{-0.08 \times 180}}
\]

Let's compute this step-by-step.After 6 months, approximately **349,805** people are expected to have acquired the virus in province X, assuming no measures were taken to prevent its spread.

Would you like more details or have any questions?

Here are some related questions:
1. What factors affect the growth rate of a virus in a population?
2. How does the logistic growth model differ from an exponential growth model?
3. What is the impact of initial population size on the spread of a virus?
4. How do real-life interventions, like social distancing, affect the logistic growth of a virus?
5. What other mathematical models can be used to predict the spread of infectious diseases?

**Tip:** Logistic growth models are particularly useful when there is a carrying capacity or a maximum limit to growth, such as a total population size.

During the start of the COVID-19 pandemic, it is assumed that the coronavirus's spread rate is 8% daily following a simple logistic growth model. There are 350 persons assumed to have acquired the virus in province X. Assuming province X with a population of 350,000 does not follow any necessary protocol to prevent the spread of the virus, approximately how many are expected to have acquired the virus after 6 months? Round off your answer to the whole number.

Calculate how many people are expected to acquire the COVID-19 virus in province X after 6 months, using the logistic growth model. This problem covers important concepts in population dynamics and mathematical modeling, suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation