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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 = 8000. (a) write an equation that expresses r as a function of x. (use k for the constant of proportionality and p for the population.) r=kx(p−x) (b) compare the rate of spread of this infection when 90 people are infected to the rate of spread when 900 people are infected. which rate is larger? by what factor? (round your answer to one decimal place.)

Respuesta :

Yna9141
a. In this item, we are given that the value of r (rate) is jointly proportional to x( infected) and p-x (not infected). This joint variation can be expressed as,
                r = k(x)(p-x)
where k is the constant of proportionality.

b. When p = 8000. 
   x = 90,
  r = k(90)(8000 - 90) = 711900k

for x = 900
  r = k(900)(8000 - 900) = 6390000k

From the obtained values, when 900 are infected then, the rate of spreading the disease is faster compared to only 90 infected.

c. factor = (6390000k / 711900 k) x 100 = 879.60%.
Hence, the disease will spread by about 8.97 times faster. 

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