Chapter 3.4, Problem 33E

Actuarial Science. An actuary works for an insurance company and calculates insurance premiums. Given an actual mortality rate (probability of death) for a given age, actuaries sometimes need to project future expected mortality rates of people of that age. For example,

$Q\left(t\right)=\left(Q_0-0.00055\right)e^{0.163t}+0.00055,$

where t is the number of years into the future and $Q_0$ is the mortality rates when $t=0,$

projects future mortality rates.

a. Suppose the actual mortality rate of a group of females aged 25 is 0.014 (14 deaths per 1000). What is the future expected mortality rate of this group of females 3, 5, and 10 yr in the future?

b. Sketch the graph of the mortality function $Q\left(t\right)$

for the group in part (a) for $0\le t\le 10$