The life expectancies for men and women in the United States can be approximated by the following formulas:
Women: E= 0.126t+76.74
Men: E=0.169t+69.11
where E represents the length of life in years and t represents the year of birth,measured as number of years since 1975.
a. Write a single equation that can be used to determine in what year of birth
the life expectancy of men and women would be the same.
b. Solve the equation in part a
c. What is the life expectancy for the year of birth determined in part b?
0.126t+76.74 = 0.169t+69.11
or
.043 t = 7.63
or
t = 177
year = 1975 + 177 = 2152
if t = 177
E = .126(177) + 76.74
E = 99.1 years old
a. To find the year of birth when the life expectancy of men and women would be the same, we need to set the two equations equal to each other:
0.126t + 76.74 = 0.169t + 69.11
b. Now we solve the equation to determine the year of birth:
Subtract 0.126t from both sides:
76.74 - 0.126t = 0.169t + 69.11 - 0.126t
Rearrange the equation by combining like terms:
76.74 - 69.11 = 0.169t - 0.126t + 0.126t
7.63 = 0.043t
Divide both sides by 0.043:
7.63 / 0.043 = t
t ≈ 177.558
So, the year of birth when the life expectancy of men and women would be the same is approximately 177.558 years after 1975. Let's call it t = 177.558 years.
c. To find the life expectancy for the year of birth determined in part b (t = 177.558), we substitute it into either of the original equations. Let's use the equation for women:
E = 0.126t + 76.74
E = 0.126(177.558) + 76.74
E ≈ 22.383 + 76.74
E ≈ 99.123
Therefore, the life expectancy for the year of birth determined in part b (t = 177.558) is approximately 99.123 years.