Problem

In 1995, the life expectancy of males in a certain country was 65.8 years. In 2002, it was 69.6 years. Let $E$ represent the life expectancy in year $t$ and let $t$ represent the number of years since 1995. The linear function $E(t)$ that fits the data is $E(t)=$ (Round to the nearest tenth.)

Solution

Step 1 :We are given two points on the line: (0, 65.8) and (7, 69.6).

Step 2 :We can use these two points to find the slope of the line, which is the change in \(E\) divided by the change in \(t\).

Step 3 :The slope is calculated as \(\frac{69.6 - 65.8}{7 - 0} = 0.5428571428571425\), which rounds to 0.5.

Step 4 :Once we have the slope, we can use the point-slope form of a line to find the equation of the line.

Step 5 :The y-intercept is the life expectancy in 1995, which is 65.8.

Step 6 :This means that the equation of the line is \(E(t) = 0.5t + 65.8\).

Step 7 :\(\boxed{E(t) = 0.5t + 65.8}\) is the final answer.

From Solvely APP
Source: https://solvelyapp.com/problems/16921/

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