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Question 285659: Life Span Some scientists believe there is a limit to how
long humans can live.* One supporting argument is that
during the last century, life expectancy from age 65 has
increased more slowly than life expectancy from birth, so
eventually these two will be equal, at which point, according
to these scientists, life expectancy should increase no
further. In 1900, life expectancy at birth was 46 yr, and life
expectancy at age 65 was 76. In 2000, these figures had
risen to 76.9 and 82.9, respectively. In both cases, the
increase in life expectancy has been linear. Using these
assumptions and the data given, find the maximum life
expectancy for humans.
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In 1900, life expectancy at birth was 46 yr, and life
expectancy at age 65 was 76. In 2000, these figures had
risen to 76.9 and 82.9, respectively. In both cases, the
increase in life expectancy has been linear. Using these
assumptions and the data given, find the maximum life
expectancy for humans.
-----------------
Life Expectancy linear function:
Two points: (0,46), (100,76.9)
slope = (76.9-46)/(100-0) = 30.9/100 = 0.309
-------
Equation:
life ex = 0.309x + 46 where x is # of years after 1900
------------------
Life Expectancy at 65 linear function:
Two points: (0,76) and (100,82.9)
slope = (82.9-76)/100 = 6.9/100 = 0.069
-------
Equation:
Expect after 65 = 0.069x+46
-------------------------------
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Cheers,
Stan H
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Some scientists believe there is a limit to how long humans can live.
One supporting argument is that during the last century, life expectancy from
age 65 has increased more slowly than life expectancy from birth, so
eventually these two will be equal, at which point, according to these
scientists, life expenctancy should increase no further.
In 1900, life expectancy at birth was 46yr, and life expectancy at age 65 was 76.
In 2000, these figures had risen to 76.9 and 82.9 , respectively.
IN both cases, the increase in life expectancy has been linear.
Using these assumptions and the data given, find the maximum life expectancy for humans.
:
Let x = number of yrs from 1900 (1900 = 0 and 2000 = 100)
:
Let y = yrs of life expected
:
Determine the "from birth" equation
x1 = 0; y1 = 46
x2 = 100; y2 = 76.9
:
Find the slope: m = (y2-y1)/(x2-x1)
m = (76.9 - 46)/(100-0) = 30.9/100 = .309 is the slope
:
Find the equation using y - y1 = m(x-x1)
y - 46 = .309(x - 0)
y = .309x + 46
:
:
Determine the "from age 65" equation (green):
x1 = 0; y1 = 76
x2 =100; y2 = 82.9
:
Find the slope:
m = (82.9-76)/(100 - 0) = 6.9/100 = .069 is the slope
Find the equation:
y - 76 = .069(x - 0)
y = .069x + 76
:
Max life expectancy is said to occur when these two lines intersect:
Age = vertical axis, year = horizontal
:
:
To solve, put equations into the standard form to solve:
-.309x + y = 46
-.069x + y = 76
-----------------subtracting eliminates y
-.24x = -30
x = -30/-.24
x = 125 yrs, (the year 2025)
:
Find the actual age this occurs, find y:
-.069(125) + y = 76
-8.625 + y = 76
y = 76 + 8.625
y = 84.625 max age
:
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