Question

A pack of 100 wolves on a remote island are suffering from a new disease. Let W(t) be the number of sick wolves at time t. Suppose that 10 wolves are sick initially and the disease is spreading at a rate proportional to the product of the time elapsed and the square root of the number of sick wolves. Give the mathematical model (IVP) for W.

a) dWdt=kW,W(0)=b) dWdt=ktW−−√,W(0)=10
c) dWdt=kW−−√,W(0)=10
d) dWdt=kW,W(0)=100
e) dWdt=kW−−√,W(0)=100
f) None of the above.

Answer 1

`b)\,(dW)/(dt)=kt√(W), \,W(0)=10`

Explanation:

Initial number of sick wolves = W(0) = 10

At time t, no. of sick wolves = W(t)

Given that disease is spreading at a rate proportional to the product of the time elapsed and the square root of the number of sick wolves:

`(dW)/(dt)=kt√(W)`

Mathematical model of above case is:

`(dW)/(dt)=kt√(W), \,W(0)=10`