SOLUTION: Life expectancies at birth for men and women can be modeled by the following functions: w(x)= 0.126x+76.74 M(x)= 0.126x+69.11 W(x) represents the life expectancy of wo

Algebra ->  Linear-equations -> SOLUTION: Life expectancies at birth for men and women can be modeled by the following functions: w(x)= 0.126x+76.74 M(x)= 0.126x+69.11 W(x) represents the life expectancy of wo      Log On


   

Question 251888: Life expectancies at birth for men and women can be modeled by the following functions:
w(x)= 0.126x+76.74
M(x)= 0.126x+69.11


W(x) represents the life expectancy of women and M(x) represents the life expectancy of men. The x represents the years since 1975. (x=0 corresponds to the year 1975, x=5 corresponds to 1980, and so on).
this goes on until 2000
x is the years since 1975. 1975 0 1985-5 1990-15 1995- 20 2000- 25
I am not understanding this I also have to figure out on a slope is the life expectantcy of men or women increasing more rapidly. then I have to determine the birth years in a inequality where the men life expectancy are greater than women

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the equation W%28x%29=0.126x%2B76.74 is in slope-intercept form y=mx%2Bb, where 'm' is the slope and 'b' is the y-intercept, this means that the slope is m=0.126.


Similarly, for M%28x%29=+0.126x%2B69.11, this equation is also in slope-intercept form y=mx%2Bb and the slope is m=0.126 as well. So the two slopes are equal.


What this means is that the life expectancies are both increasing at the same rate.


To find out which years men have a greater life expectancy than women, simply set M(x) (life expectancy of men) greater than W(x) (life expectancy of women) like this


M%28x%29%3EW%28x%29


0.126x%2B69.11%3E0.126x%2B76.74 Plug in M%28x%29=+0.126x%2B69.11 and W%28x%29=0.126x%2B76.74


1000%280.126x%2B69.11%29%3E1000%280.126x%2B76.74%29 Multiply both sides by 1000 to clear out the decimals.


126x%2B69110%3E126x%2B76740 Distribute and multiply.


126x%3E126x%2B76740-69110 Subtract 69110 from both sides.


126x-126x%3E76740-69110 Subtract 126x from both sides.


0x%3E76740-69110 Combine like terms on the left side.


0x%3E7630 Combine like terms on the right side.


0%3E7630 Simplify.


Since this inequality is NEVER true for any value of 'x', this means that the original inequality is also NEVER true.


Since there are no solutions to the original inequality, this means that the life expectancy of men will never exceed the life expectancy of women.


Note: I would make sure that you copied the problem down correctly (or ask if there are any typos).