In 1993, the life expectancy of males in a certain country was 67.2 years. In 1999, it was 70.3 years. Let E represent the life expectancy in year t and let t represent the number of years since 1993.
The linear function E(t) that fits the data is E(t)=_t + _.
(Round to the nearest tenth)
Use the function to predict the life expectancy of males in 2009.
E(16)= _
(Round to the nearest tenth)
To find the linear function that fits the given data, we need to determine the slope and y-intercept. The slope represents the rate of change in life expectancy over time, and the y-intercept represents the starting point in 1993.
To calculate the slope, we use the formula:
Slope (m) = (E(t2) - E(t1)) / (t2 - t1)
Let (t1, E(t1)) = (0, 67.2) be the point representing the year 1993, and (t2, E(t2)) = (6, 70.3) represent the year 1999. Plugging the values into the formula:
Slope = (70.3 - 67.2) / (6 - 0)
= 3.1 / 6
= 0.5167 (rounded to four decimal places)
Now, to find the y-intercept, we can use the equation of a line:
y = mx + b
Since the line passes through the point (0, 67.2), we substitute the values into the equation:
67.2 = 0.5167(0) + b
b = 67.2
Therefore, the linear function E(t) that fits the data is:
E(t) = 0.5167t + 67.2 (rounded to the nearest tenth)
To predict the life expectancy in 2009, we need to find the value of E(16) using the linear function. Substituting t = 16 into the equation:
E(16) = 0.5167(16) + 67.2
= 8.2672 + 67.2
= 75.4672 (rounded to the nearest tenth)
Therefore, the predicted life expectancy of males in 2009 is approximately 75.5 years.