A toxic chemical degrades over time and the annual dosage it produces is d(t) = exp (-0.05t) (t = years)
The annual individual fatality risk probability is R(d) = d/1000 and the loss of life cost is h = $3M per person. How much would you be willing to spend to avert this risk, if a protective measure may be added which reduces the fatality risk to zero (assume a 25 year planned storage for this toxic chemical)?
a) Integrate the annual individual fatality risk probability expression to obtain the total fatality risk accumulated over 25 years.
b) Then calculate the cost over 25 years based on the fatality probability.
c) Based on the fatality cost, state the maximum acceptable cost of a protective measure to avert this fatality risk.