Can someone help me set this up to solve or what should i do because i have no clue. thanks.
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.
The problem is based on unfounded assumptions, but that is not the problem.
You have two linear equations, and you are looking for the common point where those lines intersect.
Line1) Expectancy0= 46 + (76.9-46)/100 * year
LIne2) Expectancy65= 76 + (82.9=76)/100 * year
where year is time in years after 1900.
solve to see where expectancy0=expectance65
Can you continue helping me. I am not seeing how to bring out this problem. this is what i had in the beginning:
letting x = # of yrs from 1900 (1900=0 and 2000 = 100)
letting y = yrs of life expected
determining the "from birth" equation
x 1 = 0 ; y 1 = 46
x2 = 100;y2=76.9
i figured out slope to be:
m= (76.9-46)/(100-0)=(30.9)/(100) = 0.309
then by using equation: y-y1=m(x-x1)
y-46=0.309 (x-0)
y=0.309x + 46
then i determine "from age 65" equation
x1=0;y1 = 76
x2= 0.309; y = 82.9
finding slope
m = (82.9-76)/(100-0)=(6.9)/(100)=0.069
then i make it into the format
y-76=0.069 (x-1)
y=0.069x+76
so then by placing both equations in standard form to solve
-0.309x+y=46
-0.069x+y=76
subtracting eliminating y
-0.24x=-30
x = (-30)/(-0.24)
x= 125 yrs (yr 2025)
Actual age find y
-0.069 (125) - y = 76
-8.625 + y = 76
y=76 +8.625
y=84.625 max age
yes, that is it.
Yes, you are correct in your solution. Let me summarize the steps you took to solve the problem:
1. You defined the variables x and y as the number of years from 1900 and the years of life expected, respectively.
2. You determined the equation for life expectancy "from birth" by using the points (0, 46) and (100, 76.9). The slope of the line was calculated as 0.309. The equation for this line is y = 0.309x + 46.
3. You determined the equation for life expectancy "from age 65" by using the points (0, 76) and (0.309, 82.9). The slope of the line was calculated as 0.069. The equation for this line is y = 0.069x + 76.
4. You put both equations in standard form, resulting in the equations -0.309x + y = 46 and -0.069x + y = 76.
5. By subtracting the second equation from the first equation, you eliminated y and solved for x, which resulted in x = 125 years (year 2025).
6. Finally, you substituted the value of x into one of the equations (y = 0.069x + 76) to find the maximum life expectancy of y = 84.625 years.
Your solution is correct, and it shows that the maximum life expectancy for humans based on the given data is 84.625 years.