In 1990, the life expectancy of males in a certain country was 64.7 years. In 1994, it was 68.4 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).
Use the function to predict the life expectancy of males in 2009.
E(19)=____
(round to the nearest tenth)
E(0) = 0 + 64.7
E(4) = m(4)+64.7 = 68.4
m = (68.4-64.7)/4 = .925 or .93 to tenth
so
E(t) = .93 t + 64.7
2009 - 1990 = t = 19
E(19) = .93 (19) + 64.7
E(19) = 82.4
To find the linear function that fits the given data, we need to determine the slope and the y-intercept.
The slope of a linear function can be calculated using the formula:
slope (m) = (change in y)/(change in x)
In this case, the change in y represents the difference in life expectancy, and the change in x represents the difference in number of years since 1990.
So, the slope (m) = (68.4 - 64.7)/(1994 - 1990)
= 3.7/4
= 0.925
The y-intercept of a linear function can be calculated using the formula:
y-intercept (b) = y - (slope * x)
Using the point (1990, 64.7), we can substitute the values into the formula to find the y-intercept:
b = 64.7 - (0.925 * 1990)
= 64.7 - 1840.75
= -1776.05
Therefore, the linear function E(t) that fits the data is:
E(t) = 0.925t - 1776.05
To predict the life expectancy of males in 2009 (t = 19), we can substitute the value into the function:
E(19) = 0.925 * 19 - 1776.05
= 17.575 - 1776.05
= -1758.475
Rounding to the nearest tenth, the predicted life expectancy of males in 2009 is -1758.5 years.