in 1991 the life expectancy of males in a certain country was 73.7 years in 1997 it was 76.9 years let E represent the life expectancy in year T and let T represent the number of years since 1991

the Linear function E (T) that fits the data is E(t)=_____T+______

use the function to predict the life expectancy of males in 2008
E(17)=___________________
round to the nearest tenth

At T=0, which is when we're in 1991, we want E(0)=73.7.

The slope in front of T is found as follow :

(76.9 - 73.7) divided by (1997-1991)

= 0.53333~ = 8/15

This mean thay the life expectancy would increase by 8/15th of a year every year.

In short, E(T) = 8/15 x T + 73.7

And E(17) = 8/15 x 17 + 73.7 which you can calculate.

close, but not quite.

To find the linear function that represents the given data, we need to calculate the slope and the y-intercept.

We are given two data points:
In 1991 (T = 0), the life expectancy of males was 73.7 years (E = 73.7).
In 1997 (T = 6), the life expectancy of males was 76.9 years (E = 76.9).

To calculate the slope (m), we can use the formula:
m = (E2 - E1) / (T2 - T1)

Using the given data:
m = (76.9 - 73.7) / (6 - 0)
m = 3.2 / 6
m = 0.5333 (rounded to four decimal places)

Now let's calculate the y-intercept (b).
We can use the formula for a line: E = mT + b.
Rearranging the equation, we have: b = E - mT

Using one of the data points (1991, 73.7):
b = 73.7 - (0.5333 * 0)
b = 73.7

So, the linear function that fits the data is:
E(T) = 0.5333T + 73.7

To predict the life expectancy of males in 2008 (T = 17), we can substitute T = 17 into the equation:
E(17) = 0.5333(17) + 73.7
E(17) = 9.0656 + 73.7
E(17) = 82.7656

Therefore, the predicted life expectancy of males in 2008 is approximately 82.8 years when rounded to the nearest tenth.