answer question

Question

The rate r at which a disease spreads in a population of size P is jointly proportional to the number x of infected people and the number P − x

 who are not infected. An infection erupts in a small town with population P = 6,000.

(a)

Write an equation that expresses r as a function of x. (Use k for the constant of proportionality and P for the population.)

Answer 1

You're given that the rate of spread is proportional to both the number of people infected and the number of healthy people. This makes sense because for the disease to spread, an infected and a healthy person need to come into contact with each other.

You're looking for an expression of the form (constant)×(infected people)×(healthy people).

Note the the quantity they give P - x represents the number of healthy people.

I hope this helps. I can't go any further or I'd be doing your homework for you.