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

Answer:

$b)\,\frac{dW}{dt}=kt\sqrt{W}, \,W(0)=10$

Step-by-step 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:

$\frac{dW}{dt}=kt\sqrt{W}$

Mathematical model of above case is:

$\frac{dW}{dt}=kt\sqrt{W}, \,W(0)=10$