Question

An infection is transferred such that the rate of the number of people infected, N, can be modelled by dN/dt = 0.16t where t is the number of days after exposure to the infection. In a school of 800 students, how many students will not be infected after 20 days?

Answer 1

\[\begin{align*}\frac{dN}{dt}&=0.16t\\
dN&=0.16t~dt\\
\int dN&=0.16\int t~dt\\
N&=0.08t^2+C\end{align*}\]
We're going to need the value of \(C\) to determine what we want to find, but we can't do that without an initial condition. Do we know how many students are infected at the start?

Answer 2

nope, thats all that was given

Answer 3

@saifoo.khan

Answer 4

In that case, I suppose we can assume the number of infected at the start is at least 1, and no more than 800.

Answer 5

okay

Answer 6

So if we assume \(N(0)=1\) then you have
\[1=0.08(0)^2+C~~\Rightarrow~~C=1\]

Answer 7

After 20 days, i.e. at \(t=20\), you have
\[N(20)=0.08(20)^2+1=33\]
Out of the 800 students, that would leave 767 uninfected remaining.

But again, it depends on the initial conditions.

Answer 8

Thank you for your help :)

Answer 9

yw