a male born in 1975 does not want his future wife to outlive him. What should be the year of birth for his wife so that they both can be expected to die in the same year?
Find M(y)+F(y) to get the formula for life expectancy of a person born in year y
2
M (1975)
F (1975)
F (1975) - M (1975)
M(y) = 0.16252y - 251.91
F(y) = 0.18268y - 284.98
To find the year of birth for the wife, we need to set up an equation where the life expectancy of the male is equal to the life expectancy of the female.
Using the formulas for life expectancy:
M(y) = 0.16252y - 251.91
F(y) = 0.18268y - 284.98
Let's assume the year of birth for the wife is W(y).
We want the male and female to die in the same year, so we set up the equation:
M(1975) + (W(y) - 1975) = F(W(y))
Substituting the formulas for M(y) and F(y) into the equation:
(0.16252 * 1975 - 251.91) + (W(y) - 1975) = 0.18268 * W(y) - 284.98
Simplifying:
(0.16252 * 1975 - 251.91) + W(y) - 1975 = 0.18268 * W(y) - 284.98
Combining like terms:
0.16252 * 1975 - 251.91 - 1975 + 284.98 = 0.18268 * W(y) - W(y)
Simplifying further:
356.42 = (0.18268 - 1) * W(y)
Simplifying again:
356.42 = -0.81732 * W(y)
Finally, solving for W(y):
W(y) = 356.42 / -0.81732
Using a calculator, we find:
W(y) ≈ -435.72
The year of birth for the wife cannot be a negative number, so it is not possible for both the male and female to be expected to die in the same year.