in 1991 the life expectancy of males in a certain country was 68.2 years. in 1995 it was 70.8 years. let e represent the life expectancy in year t and let t represent the number of years since 1991
look at it as two ordered pairs (0,68.2) and (4,70.8)
find the equation in the form
e = mt + b, just like you would find the equation of the line y = mx + b
since (0,68.2) is the y-intercept
you already know
e = mt + 68.2
just find the slope m and you are done
To find the equation that represents the life expectancy in terms of the number of years since 1991, we can use the given data points.
Let's start by assigning variables to the given information:
- Let "e" represent the life expectancy in year "t."
- Let "t" represent the number of years since 1991.
According to the data:
- In 1991, the life expectancy for males was 68.2 years. This can be expressed as e = 68.2 when t = 0.
- In 1995, the life expectancy for males was 70.8 years. This can be expressed as e = 70.8 when t = 4.
Now we need to determine the relationship between e and t. In this case, we can use linear interpolation to find the equation.
First, we need to find the slope (m) of the line using the formula:
m = (change in y) / (change in x)
change in y = e2 - e1 = 70.8 - 68.2 = 2.6
change in x = t2 - t1 = 4 - 0 = 4
So, the slope is:
m = (2.6) / (4) = 0.65
Next, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (0, 68.2) on the line, we can substitute the variables:
e - 68.2 = 0.65(t - 0)
Simplifying the equation:
e - 68.2 = 0.65t
Finally, let's isolate e by adding 68.2 to both sides:
e = 0.65t + 68.2
So, the equation that represents the life expectancy (e) in terms of the number of years since 1991 (t) is:
e = 0.65t + 68.2