In 1991 the life expectancy of males in a certain country was 73.7 years old, In 19951995 it was 77.4 years. Let E represent the life expectancy in year (t) and let (t) represent the number of years
since 1991 What is the linear function fits the data. Use the function to predict the life expectancy of males in 2008
let 1991 be t=0
then 1991 life exp ---> (0,73.7)
and 1995 life exp ----> (4,77.4)
slope = (77.4 - 73.7)/4 = .925
E(t) = .925t + 73.7
2008 ----> t = 17
E(17) = .925(17) + 73.7 = 89.425
What is the name of that country? Utopia?
Sounds like it doesn't it? I have been working nights and trying to get this assignment done sometimes the simplest thing seems way too hard. I appreciate your help, Shauna
To find the linear function that fits the given data, we need to find the equation of a straight line.
We have two data points:
(0, 73.7) - this represents the year 1991
(4, 77.4) - this represents the year 1995
Using the formula for the equation of a line (y = mx + b), where y is the dependent variable (life expectancy), x is the independent variable (years since 1991), m is the slope of the line, and b is the y-intercept, we can calculate the equation.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
= (77.4 - 73.7) / (4 - 0)
= 3.7 / 4
= 0.925
Now we have the slope (m). To find the y-intercept (b), we can substitute one of the given points into the equation and solve for b:
73.7 = (0.925 * 0) + b
73.7 = b
Now we know the slope (m = 0.925) and the y-intercept (b = 73.7). The equation of the linear function is:
E = 0.925t + 73.7
To predict the life expectancy of males in 2008, we need to find t (the number of years since 1991) for the year 2008. Since 2008 is 17 years after 1991, we substitute t = 17 into the equation:
E = 0.925(17) + 73.7
E = 15.725 + 73.7
E = 89.425
Therefore, the predicted life expectancy of males in 2008 is approximately 89.4 years.