SOLUTION: A life insurance table indicates that a woman who is now A years old can expect to live E years longer. Suppose that A and E are linearly related and that E=50 when A=24 and E=20 w

Question 198329: A life insurance table indicates that a woman who is now A years old can expect to live E years longer. Suppose that A and E are linearly related and that E=50 when A=24 and E=20 when A=60.
a. At what age may a woman except to live 30 years longer?
b. What is the life expectancy of a newborn female child?
c. At what age is the life expectancy zero?
Please help to solve the above problem. Help is appreaciated.
Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A life insurance table indicates that a woman who is now A years old can expect to live E years longer. Suppose that A and E are linearly related and that E=50 when A=24 and E=20 when A=60.
You have two points: (24,50), (60,20)
a. At what age may a woman except to live 30 years longer?
slope = (50-20)/(24-60) = 30/-36 = -5/6
------
intercept: 20 = (-5/6)60 + b
b = 20 + 50 = 70
---
Equation: E(A) = (-5/6)A + 70
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b. What is the life expectancy of a newborn female child?
E(0) = (-5/6)*0 + 70 = 70 years
-------------------------------------------
c. At what age is the life expectancy zero?
(-5/6)A + 70 = 0
(-5/6)A = -70
A = (6/5)*70
A = 6*14 = 84 (life expectancy is zero at age 84)
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Cheers,
Stan H.

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