Reference no: EM131607345

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.