Some scientists believe there is a limit to how long humans can live. One suppor

Question

Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past 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 48 years, and life expectancy at age 65 was 78 yr In 2010, these figures had risen to 78 5 and 84.4, 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. Find the linear equations for life expectancy at birth and life expectancy at age 65. Set the x-value (5me in years) for 1900 to 0. The linear equation for life expectancy at birth is y = and the near equation for life expectancy at age 65 is y = where y is the life expectancy in years and x is the year (1900-0) in both cases. (Type your answers in slope-intercept form. Use integers or decimals for any numbers in the equations. Round to three decimal places as needed.)

Explanation / Answer

Let x = number of years from 1900 (1900 = 0 and 2010 = 110)
Let y = years of life expected

From birth equation x1 = 0; y1 = 48
x2 = 110; y2 = 78.5

Life Expectancy linear function:

y = mx +c

m = (y2-y1)/(x2-x1) = 0.27

y = 0.27x + 48 ----- (i)

Now solving for Life Expectancy at 65 linear function:

(x1,y1) = (0,78)

(x2,y2) = (110,84.4)

y = mx + c

m = (84.4-78)/(110) = 0.058

y = 0.058 x + 78 ---- (ii)

Max life expectancy is will to occur when these two lines intersect:

Solving the two equations

y = 0.058 x + 78

y = 0.27x + 48

x = 141.5 ( in the year 2010 + 141.5 = 2151 )

y = 86.2 is the maximum age

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