Answer the questions in Exercise 36 for a country whose life expectancy function is

Data from Exercises 36

In a certain undeveloped country, the life expectancy of a person t years old is L(t) years, where L(t) = 41.6(1 + 1.07t)^0.13

a. What is the life expectancy of a person in this country at birth? At age 50?

b. What is the average life expectancy of all people in this country between the ages of 10 and 70?

c. Find the age T such that L(T) = T. Call T the life limit for this country. What can be said about the life expectancy of a person older than T years?

d. Find the average life expectancy L_e over the age interval 0 ≤ t ≤ T. Why is it reasonable to call L_e the expected length of life for people in this country?

L(t) = 0.015t 110e 1 + e0.015t