In 1991, the life expectancy of males in a certain country was 67.2 years. In 1995, it was 71.1 years. Let E represent the life expectancy in year t and let t represent the number of years since 1990.
The linear function E(t) that fits the data is
E(t) =?t + ?
(Round to the nearest tenth)
you will find that the question contained in
http://www.jiskha.com/display.cgi?id=1305681090
has the same setup as yours, just change the numbers and follow my method.
To find the linear function E(t) that fits the data, we need to determine the slope and the y-intercept.
Let's start by finding the slope. The slope is the change in y (life expectancy) divided by the change in x (number of years since 1990).
The change in y is given by the difference in life expectancies between 1995 and 1991:
Change in y = 71.1 years - 67.2 years = 3.9 years
The change in x is the number of years between 1995 and 1991:
Change in x = 1995 - 1991 = 4 years
Now we can calculate the slope:
Slope = Change in y / Change in x = 3.9 years / 4 years = 0.975
Next, we can find the y-intercept. The y-intercept is the value of E(t) when t = 0 (which corresponds to the year 1990). In this case, the life expectancy in 1990 is not given directly, but we can calculate it by subtracting 1990 from 1991 and multiplying the result by the slope:
Life expectancy in 1990 = Life expectancy in 1991 - (1991 - 1990) * slope
Life expectancy in 1990 = 67.2 years - (1991 - 1990) * 0.975
Life expectancy in 1990 = 67.2 years - 1 * 0.975
Life expectancy in 1990 = 67.2 years - 0.975 years
Life expectancy in 1990 = 66.225 years
Now we have the slope (0.975) and the y-intercept (66.225), and we can write the equation in the form E(t) = mt + b, where m is the slope and b is the y-intercept:
E(t) = 0.975t + 66.225
Therefore, the linear function E(t) that fits the data is E(t) = 0.975t + 66.225.