Let I be the number of individuals infected with the disease and let s be the speed at which the speed spreads. We know that the speed is proportional to the number of people infected, which means that we have a relation between the variables of the form:
[tex]s=kI[/tex]
where k is the proportionality factor. To find the proportionality we plug the values given of the population and the speed, that is, we plug s=12 and I=600 in the equation and solve for t:
[tex]\begin{gathered} 12=600k \\ k=\frac{12}{600} \\ k=\frac{1}{50} \end{gathered}[/tex]
Hence the proportionality factor is 1/50; plugging it in the equation we conclude that the formula of the speed as a fucntion of the number of infected people is:
[tex]s=\frac{1}{50}I[/tex]
