We answer the first part of the problem here.
`P = 50000`, so our differential equation becomes:
Solving using Scientific Notebook gives us the number of people affected at time t:
`A(t)=(50\ 000)/(1+499e^(-50\ 000ct))`
[We'll see how to solve this kind of problem in the Separation of Variables page, later in this chapter.]
Now, we are told that at `t = 10`, `A = 1000`.
So now we can substitute and solve for `c`:
`c = 4. 6416 xx 10^-6`
So substituting this value of c into the expression for A(t) gives us: