In 1994, the life expectancy of males in a certain country was 65.7 years. In 2000, it was 69.0 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994
the linear function E(t) that fits the data is
E(t)=?t+?
use the function to predict the life expectancy of males in 2007?
E(13)=?
slope= 69-65.7 divided by 6 years
E(t)= slope*t+ b
To find b, put in 1994, the slope, t=0, and you have b. (65.7)
72.85
To find the linear function E(t) that fits the given data, we need to determine the slope and y-intercept of the line.
Given that in 1994 (t = 0), the life expectancy is 65.7 years, and in 2000 (t = 6), the life expectancy is 69.0 years, we can use these two data points to find the slope (m) and y-intercept (b) of the line.
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values:
m = (69.0 - 65.7) / (6 - 0)
m = 3.3 / 6
m = 0.55
Now that we have the slope, we can use the point-slope form of a linear equation to find the y-intercept.
The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (0, 65.7), we substitute the values into the equation:
y - 65.7 = 0.55(x - 0)
y - 65.7 = 0.55x
y = 0.55x + 65.7
Therefore, the linear function E(t) that fits the data is:
E(t) = 0.55t + 65.7
To predict the life expectancy of males in 2007 (t = 13), we can substitute the value into the equation:
E(13) = 0.55(13) + 65.7
E(13) = 7.15 + 65.7
E(13) = 72.85
Therefore, the predicted life expectancy of males in 2007 is 72.85 years.