Question 302169: in 1992 life expectancy of males was 69.1 years in 1996 it was 72.9 years let e represent the life expectancy in year t and let t represent the # of years since 1992.
I do not need the problem solved only the linear function that fits the data given (Ihave trouble figuring out the formulas of word problems but once I have that I do well at figuring them out).
I have so far:
E(t) = ?t + ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If you make 1992 = 0, the 1996 should equal to 4 because 1996 - 1992 = 4 and 4 - 0 = 4.
You have 2 points of data.
They are:
(0,69.1)
(4,72.9)
If you let x = number of years and y = age expectancy, then you have an equation that looks like:
y = m*x + b
The slope of this equation is m which would be the change in life expectancy divided by the change in years.
Using your 2 points of data, this would become:
(72.9 - 69.1) / (4 - 0) = 3.8 / 4 = .95
This means that the life expectancy increases by .95 years every year.
4 * .95 = 3.8.
You start with 69.1 in year 0 and 4 years later you have 69.1 + 3.8 = 72.9
Now that you have the slope, you can fill that in the equation to get:
y = .95*x + b
b is the y-intercept.
You already know that b will be 69.1, but you can also solve for it to confirm.
You can pick either of the 2 points to replace x and y with in the equation to solve for b.
pick the point (0,69.1).
y = .95*x + b becomes 69.1 = .95*0 + b which becomes b = 69.1.
Your equation becomes y = .95*x + 69.1
Now you can set y equal to e(x) which makes your equation equal to e(x) = .95*x + 69.1
If you want to change x to t, then your equation becomes e(t) = .95*t + 69.1
Either way, that's your equation.
The key to solving this problem is to determine from the data that is given, the change in life expectancy per year.
That was done when we solved for the slope of the equation of the straight line above.
The slope was the change in life expectancy divided by the change in years which resulted in the change in life expectancy per year.
|
|
|
