Question: Consider a population of individuals with a disease. Suppose that t is the number of years since the onset of the disease. The death density function, f(t) = cte-kt, approximates the fraction of the sick individuals who die in the time interval [t, t + Δt] as follows:
Fraction who die ≈ f(t)Δt = cte-ktΔt
where c and k are positive constants whose values depend on the particular disease.
(a) Find the value of c in terms of k.
(b) If 40% of the population dies within 5 years, find c and k.
(c) Find the cumulative death distribution function, C(t). Give your answer in terms of k.