In 1993, the life expectancy of males in certain countires was 62.3. In 1999, it was 66.1 years. Let E repesent the life expectancy in year t and let t represent the number of years since 1993. The linear funtion that fits the data E(t) =
To find the linear function that fits the given data, we can use the formula for the equation of a straight line:
y = mx + b
Here, y represents the life expectancy, x represents the number of years since 1993, m represents the slope of the line, and b represents the y-intercept.
Given that in 1993, the life expectancy was 62.3 (E(0) = 62.3) and in 1999, it was 66.1 (E(6) = 66.1), we can use these two points to calculate the slope.
First, we need to find the change in y (life expectancy) and the change in x (years) between the two points:
Change in y = 66.1 - 62.3 = 3.8
Change in x = 6 - 0 = 6
Now, let's calculate the slope (m):
m = (Change in y) / (Change in x) = 3.8 / 6 = 0.633333333
Next, we can substitute the values for m and one of the points (we'll use the point (0, 62.3)) into the equation y = mx + b to solve for b:
62.3 = 0.633333333 * 0 + b
62.3 = b
Therefore, the y-intercept (b) is 62.3.
Now we can substitute the values for m and b into the equation y = mx + b to get the linear function:
E(t) = 0.633333333t + 62.3
So, the linear function that fits the given data is E(t) = 0.633333333t + 62.3.