Question

The rate R that a certain disease spreads is proportional to the number of infected individuals and is also proportional to the number of uninfected individuals. The total population is P and the number of infected individuals is D. Express the rate that the disease spreads in terms of this information. Use C as your proportionality constant.

Answer 1

Answer:

The rate of spread of disease is:

$R = CD(P-D)$                  

Step-by-step explanation:

We are given the following information:

The rate R that a certain disease spreads is proportional to the number of infected individuals and is also proportional to the number of uninfected individuals.

Total Population = P

Number of infected population = D

Number oh uninfected population = P - D

It is given that:

$R \propto D\\R \propto P-D\\\Rightarrow R \propto D(P-D)\\\Rightarrow R = CD(P-D).\\\text{where C is the constant of proportionality.}$

Thus, the rate of spread of disease is:

$R = CD(P-D)$

Answer 2

The rate of spread of the disease interms of the number of infected and uninfected persons is R =CD(T - D)

Total population, P

Number of infected individuals, D

Proportionality Constant, C

Rate, R

Using the information ;

Number of uninfected individuals = (Total population - Number of infected individuals)

Therefore,

Number of uninfected individuals = T - D

Rate α number of infected individuals α number of uninfected individuals

R α D α (T - D)

R = C × D × (T - D)

R = CD(T - D)

THEREFORE, the rate of spread of the disease in terms of C can be expressed as R = CD(T - D)

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