i need help understanding this question? can some one tell me what exactly i have to do in it
7. Suppose a student carrying a flu virus returns to an isolated
college campus of 1000 students. Determine a differential
equation for the number of people x(t) who have
contracted the flu if the rate at which the disease spreads
is proportional to the number of interactions between the
number of students who have the flu and the number of
students who have not yet been exposed to it.
If w is proportional to u and v, then w = kuv. So, we are told that
dx/dt = kx(1000-x)
I have set it up so that
"the rate at which the disease spreads is proportional to the number of students who have the flu and the number of
students who do not yet have it.
I have no way of estimating how many have been exposed to it, or determining the students' interactions. A poorly worded question. Maybe you have further insight.
To understand this question, let's break it down step by step:
1. Context: The question is asking you to determine a differential equation for the number of people who have contracted the flu on an isolated college campus.
2. Initial information: The college campus has 1000 students, and there is one student carrying a flu virus.
3. Definition: Differential equations are mathematical equations that involve rates of change and are used to solve problems involving dynamic systems.
4. Modeling the spread of the flu: The question provides a clue on how to model the spread of the flu. It states that the rate at which the disease spreads is proportional to the number of interactions between the students who have the flu and the students who have not yet been exposed to it.
5. Variables: Let's define the variables we will need for this problem:
- x(t): Number of people who have contracted the flu at time t.
- y(t): Number of people who have not been exposed to the flu at time t.
6. Differential equation: Based on the given information, we can write the differential equation. The rate at which the disease spreads is proportional to the product of x(t) and y(t). In other words, the rate of change of x(t) is equal to a constant times x(t) times y(t).
dx(t)/dt = k * x(t) * y(t)
Here, k represents the proportionality constant.
By following these steps, you can understand the question and determine the differential equation for the spread of the flu on the isolated college campus.