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 61
Ok is this one right now?
Your equation does not produce the given data values
since you want this to be linear,
treat it as if you are given two ordered pairs
(1993,61.3) and (1999,64.7)
the slope of that is 3.4/6 or 17/30
so the equation would be
E(t) = (17/30)t + b
sub in first point
61.3 = (17/30)(1993) + b
b = -32042/30
(I tested for the second point, it works)
so E(t) = (17/30)t - 32042/30
so if t = 2003
E(2003) = (17/30)(2003) - 32042/30
= 66.97 or
= 67.0 using 3 significant digits.
To determine if the given linear function is correct, we need to check if it accurately represents the change in life expectancy over time based on the given data points.
We are given two data points: in 1993, the life expectancy was 61.3 years (t=0), and in 1999, it was 64.7 years (t=6).
To find the slope of the linear function (m), we can use the formula:
m = (E2 - E1) / (t2 - t1),
where E1 and E2 are the respective life expectancies corresponding to the given years t1 and t2.
Using the data:
m = (64.7 - 61.3) / (6 - 0) = 3.4 / 6 = 0.5667.
Now we need to find the y-intercept (b) of the linear function. Since the line passes through the point (0, 61.3), we can substitute these coordinates into the equation E(t) = mt + b and solve for b:
61.3 = 0.5667 * 0 + b,
b = 61.3.
Therefore, the linear function E(t) = 0.5667t + 61.3 represents the change in life expectancy over time based on the given data points.
Now, let's use this linear function to predict the life expectancy in 2003 (t = 10):
E(10) = 0.5667 * 10 + 61.3,
E(10) = 5.667 + 61.3,
E(10) = 67.967.
According to the linear function, the predicted life expectancy in 2003 is 67.967 years.