In 1991, the life expectancy of males in a certain country was 72.8 years. In 1995, it was 75.9 years. Let E represent the life expectancy in year T and let T represent the number of years since 1991.
The linear function E(t) that fit the data is E(t)=___T+___(Round to the nearest tenth.) Use the function to predict the life expectancy of males in 2003.
E(12)=___ (Round to the nearest tenth.)
I will be happy to critique your thinking.
To find the equation that represents the linear relationship between the life expectancy E and the number of years since 1991 T, we can use the formula for the equation of a straight line:
E(t) = mx + b
Where m is the slope of the line, and b is the y-intercept.
To find the slope (m), we need two points on the line. In this case, we have two points: (0, 72.8) in 1991 and (4, 75.9) in 1995. Since T represents the number of years since 1991, we can calculate the change in T and E as:
Change in T = 4 - 0 = 4
Change in E = 75.9 - 72.8 = 3.1
Now we can calculate the slope (m) using the formula:
m = change in E / change in T
m = 3.1 / 4
m = 0.775
Now that we have the slope, we can use either of the given points to calculate the y-intercept (b). Let's use the point (0, 72.8):
E(0) = m(0) + b
72.8 = 0.775(0) + b
72.8 = b
So the y-intercept (b) is equal to 72.8.
Now we can substitute the values of m and b back into the equation to get our final linear function E(t):
E(t) = 0.775T + 72.8
Now to predict the life expectancy of males in 2003, we need to substitute T = 12 into the equation:
E(12) = 0.775(12) + 72.8
E(12) = 9.3 + 72.8
E(12) = 82.1
Therefore, the predicted life expectancy of males in 2003 is 82.1 years.