In 1990, the life expectancy of males in a certain country was 62.1 years, it was 65.3 years. Let E represent life expectancy in year T and let t represent the number of years since 1990. E(t)= [ ]t+[] use the function to predict the life expectancy of males in 2006. E(16)= [ ]
To find the function that represents the life expectancy of males in the given country, we need to determine the linear equation that relates the life expectancy to the number of years since 1990.
Given that in 1990 the life expectancy was 62.1 years and in 2006 it was 65.3 years, we can use this information to construct the equation.
Let's start by finding the slope of the line:
Slope (m) = (change in y) / (change in x) = (change in life expectancy) / (change in years)
Change in life expectancy = 65.3 years - 62.1 years = 3.2 years
Change in years = 2006 - 1990 = 16 years
m = (3.2 years) / (16 years) = 0.2
Now that we have the slope, we can use the point-slope form of a linear equation to find the y-intercept (b):
y - y1 = m(x - x1)
E - 62.1 = 0.2(t - 0)
Since t represents the number of years since 1990, when t = 0, E = 62.1.
E - 62.1 = 0.2t
E = 0.2t + 62.1
So, the function that represents the life expectancy of males in this country is E(t) = 0.2t + 62.1.
To predict the life expectancy of males in 2006 (16 years since 1990), we can substitute t = 16 into the equation:
E(16) = 0.2(16) + 62.1
E(16) = 3.2 + 62.1
E(16) = 65.3
Therefore, the predicted life expectancy of males in 2006 is 65.3 years.