In 1993, the life expectancy of males in a certain country was 61.3 years. In 1999, it was 64.7 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?
answer: E(t)=-0.03t+61.3
use function to predict life expectancy in 2003
answer: 61.6
Isn't the first term negative.
yes so the answer would be 61 correct?
To find the linear function E(t) that fits the given data, we can use the concept of linear regression. Linear regression helps us find the line of best fit for a given set of data points. In this case, we have two data points: (0, 61.3) and (6, 64.7), representing the life expectancy in 1993 and 1999, respectively.
First, we need to find the slope of the line. The formula for slope, m, is given by:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the data points into the formula, we get:
m = (64.7 - 61.3) / (6 - 0)
= 3.4 / 6
= 0.5667
Next, we need to find the y-intercept, b, which represents the value of E(t) when t = 0. We can use one of the data points and the slope to find the value of b. Let's use the point (0, 61.3):
61.3 = 0.5667(0) + b
b = 61.3
Now we have the slope and the y-intercept, which we can use to write the equation of the linear function:
E(t) = mt + b
E(t) = 0.5667t + 61.3
To predict the life expectancy in 2003, we need to find the value of E(t) when t = 10 (since 2003 is 10 years after 1993):
E(10) = 0.5667(10) + 61.3
= 5.667 + 61.3
= 67.967
Therefore, the predicted life expectancy in 2003 is 67.967 years.