Chapter 13.5, Problem 42E

(a)

To determine

To calculate: The solution of the differential equation $\frac{dx}{x\left(1000-x\right)}=kdt$ if $k=0.001$. When the specific community of 1000 people those are suffering from several disease is exposed when one of the member returns carrying the disease.

Where, x represents the number of people infected by the disease at any time t (in days).

(b)

To determine

To calculate: The time before half the population of the community is affected Where the specific community of 1000 people those are suffering from several disease is exposed when one of the member returns carrying the disease.

(c)

To determine

To calculate: The rate of new cases $\frac{dx}{dt}$ for every alternate days till first 13 days Where the specific community of 1000 people those are suffering from several disease is exposed when one of the member returns carrying the disease and differential equation is given by $\frac{dx}{x\left(1000-x\right)}=kdt$ if $k=0.001$.