A survival function is given by S0 t101t for 0t100 Improved

A survival function is given by S_0 (t)=1-.01t, for 0t100. Improved medical conditions result in a new survival pattern given by S_0 (t)=1-kt, for 0t1/k. For a life age 30, the improved medical conditions increase the complete expectation of life by four years. Find the value of k.

Solution

earlier S at t=30 yrs=1-0.01*30=0.7

S after improved medical at t=30= 1-30k

now at 30, improvement is 4 years that survival chance increased=4/30

now 1-30k-0.7=4/30

k=5/900= 0.0055