Answer:
Expression: N = C·L·l(t)· T + 20
The initial value problem and solution are expressed as a first order differential equation.
Step-by-step explanation:
First, gather the information:
total population, N = 2 000
Proportionality constant, C = 0.0002
l(t) number of infected individuals = l(t)
healthy individuals = L
The equation is given as follows:
N = C·L·l(t)
However, there is a change with time, so the expression will be:
[tex]\frac{dN}{dt}[/tex] = C·L·l(t)
multiplying both sides by dt gives:
dN = C·L·l(t)
Integrating both sides gives:
[tex]\int\limits^a_b {dN} \, dt[/tex] = [tex]\int\limits^a_b {CLl(t)} \, dt[/tex]
N = C·L·l(t)· T + K
initial conditions:
T= 0, N₀ = (0.01 ₓ 2 000) = 20
to find K, plug in the values:
N₀ = K
20 = K
At any time T, the expression will be:
N = C·L·l(t)· T + 20 Ans
