The logistic differential equation models the spread of an illness, and as time increases, the total number of reported cases approaches the limiting value of 1400.
The correct answer is option B.
The given differential equation dy/dt = (1/5600) * y * (1400 - y) models the spread of an illness in a large city over time. To find the limiting value as time (t) increases, we examine the behavior of the solution y(t).
The logistic differential equation has two equilibrium solutions: y = 0 and y = 1400. When y = 0, the derivative dy/dt is zero, indicating no growth. Similarly, when y = 1400, the derivative is also zero, representing the limiting value where the spread of the illness reaches saturation.
Given the initial condition y(0) = 5, the solution y(t) approaches the limiting value of 1400 as time t increases. Therefore, the answer is:
B. 1400
The question probable may be:
The total number of reported cases of an illness in a large city t days after of an outbreak is modeled by the function y= F(t) that is a solution to the logistic differential equation dy/dt = 1/5600 y(1400-y). If there are 5 reported cases of the illness initially, what is the limiting value for the total number of reported cases of illness as t increases.
A. 700
B. 1400
C. 2800
D. 5600