In 1992 the life expectancy of males in a certain country was 63.4 years. In 1997 it was 66.7 years, let E represent the life expectancy in year t and let t represent the number of years since 1992. The linear equation that fits the data is E(t)+ t round to the nearest tenth. use the function to predict the life expectancy of males in 2005.
To find the linear equation that fits the given data, we need to determine the equation in the form of E(t) = mt + b, where m represents the slope and b represents the y-intercept.
We are given two points: (0, 63.4) and (5, 66.7). These points represent the years 1992 and 1997, respectively. We can use these points to calculate the slope of the line.
First, let's calculate the slope (m):
m = (E2 - E1) / (t2 - t1)
m = (66.7 - 63.4) / (5 - 0)
m = 3.3 / 5
m = 0.66
Next, we need to find the y-intercept (b). We can use either of the given points to do this calculation. Let's use (0, 63.4):
E = mt + b
63.4 = 0.66(0) + b
63.4 = b
Now we have the slope (m = 0.66) and the y-intercept (b = 63.4). The linear equation that fits the data is:
E(t) = 0.66t + 63.4
To predict the life expectancy in 2005 (t = 2005 - 1992 = 13), we substitute t = 13 into the equation:
E(13) = 0.66(13) + 63.4
E(13) = 8.58 + 63.4
E(13) ≈ 71.0
Therefore, the predicted life expectancy of males in 2005 is approximately 71.0 years.