I am lost, and I bet it is simple, but I have been working with many problems and I keep coming back to this and I grow increasingly confused. How do I begin to solve this problem?
In 1993 the life expectancy of males in a certain country was 71.7 years. In 1997 it was 75.2 years. Let E represent the life expectancy in years t and let t represent the number of years since 1993
The linear function that fits this data is?
E(t)=
I need to fill the above function, but confused on what data to use
The second part is
Use the formula below to predict the life expectancy of males in 2004
E (14) =
Look for the answer to this problem that I posted yesterday. How many times have you posted this question?
To solve this problem, you need to find a linear function that represents the relationship between the life expectancy (E) and the number of years since 1993 (t), using the given data points from 1993 and 1997.
To begin, let's first determine the slope of the linear function. The slope is calculated by subtracting the initial life expectancy from the final life expectancy and dividing it by the difference in years.
Slope (m) = (Final Life Expectancy - Initial Life Expectancy) / (Final Year - Initial Year)
Using the given data:
Initial Life Expectancy = 71.7 years (in 1993)
Final Life Expectancy = 75.2 years (in 1997)
Initial Year = 1993
Final Year = 1997
Slope (m) = (75.2 - 71.7) / (1997 - 1993)
= 3.5 / 4
= 0.875
Now that we have the slope (m), we can use the point-slope form of a linear equation to find the equation of the line.
Point-Slope Form: y - y1 = m(x - x1)
Using the point (x1, y1) = (1993, 71.7) and slope (m) = 0.875:
E - 71.7 = 0.875(t - 1993)
Simplifying the equation:
E - 71.7 = 0.875t - 0.875*1993
E = 0.875t + (0.875*1993) + 71.7
E(t) = 0.875t + 1742.875 + 71.7
Therefore, the linear function that fits this data is:
E(t) = 0.875t + 1814.575
To predict the life expectancy of males in 2004 using the given formula E(14), simply substitute t = 14 into the equation:
E(14) = 0.875(14) + 1814.575
E(14) = 12.25 + 1814.575
E(14) = 1826.825