In 1994, the life expectancy of males in a certain country was 63.8 years. In 2001, it was 66.0 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?
Use the function to predict the life expectancy of males in 2004?
To find the linear function that fits the given data, we can use the slope-intercept form of a linear equation, which is y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope, and b represents the y-intercept.
In this case, the dependent variable is the life expectancy (E) and the independent variable is the number of years since 1994 (t). We are given two data points: (t1, E1) = (0, 63.8) in 1994 and (t2, E2) = (7, 66.0) in 2001.
First, we find the slope (m) using the formula:
m = (E2 - E1) / (t2 - t1)
Plugging in the values, we have:
m = (66.0 - 63.8) / (7 - 0)
= 2.2 / 7
= 0.3143 (rounded to four decimal places)
Next, we substitute one of the data points (t1, E1) into the slope-intercept form and solve for the y-intercept (b). Using (t1, E1) = (0, 63.8), we have:
63.8 = 0.3143 * 0 + b
63.8 = b
Therefore, the y-intercept (b) is 63.8.
Now we can write the linear function e(t) that fits the data:
e(t) = 0.3143t + 63.8
To predict the life expectancy of males in 2004 (t = 10), we substitute t = 10 into the equation:
e(10) = 0.3143 * 10 + 63.8
= 3.143 + 63.8
= 66.943 (rounded to three decimal places)
Therefore, the predicted life expectancy of males in 2004 is approximately 66.943 years.