SOLUTION: 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

SOLUTION: 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 e

Question 182571: 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 = 3000.

(a) Write an equation that expresses r as a function of x. Use k for the constant of proportionality.
r =
(b) Compare the rate of spread of this infection when 40 people are infected to the rate of spread when 1000 people are infected. Which rate is larger? By what factor? (Give your answer correct to one decimal place.)
The rate when 1000 people are infected or the rate when 40 people are infected? by what factor?
(c) Calculate the rate of spread when the entire population is infected.

Why does this answer make intuitive sense?
i cant figure this out! help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 = 3000.
(a) Write an equation that expresses r as a function of x. Use k for the constant of proportionality.
---
r = k[x(p-x)]
----
(b) Compare the rate of spread of this infection when 40 people are infected to the rate of spread when 1000 people are infected. Which rate is larger? By what factor? (Give your answer correct to one decimal place.)
---
If x = 40, r = k[40(3000-40)] = k(118400)
Note: That doesn't make much. Are you sure you correctly posted
a statement of the relation of "r" to x and to "p-x"?
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Cheers,
Stan H.

The rate when 1000 people are infected or the rate when 40 people are infected? by what factor?

(c) Calculate the rate of spread when the entire population is infected.
Why does this answer make intuitive sense?

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