In 1991, the life expectancy of males in a certain country was 70.8 years. In 1995, it was 74.6 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)=
(Round to the nearest tenth)

E=a*t+b

in 1991,
E=a*0 + b
70.8=b
in 1995
E=a*t+b
74.6=a*(1995-1991)+70.8
solve for a, then you have the equation for E(t).

To find the linear function that fits the given data, we can use the concept of slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept.

Given data:
In 1991 (t = 0), life expectancy (E) = 70.8 years.
In 1995 (t = 4), life expectancy (E) = 74.6 years.

We need to find the slope (m) and y-intercept (b) to form the linear function.

Slope (m):
The slope (m) can be calculated using the formula:
m = (E2 - E1) / (t2 - t1),
where (E2, t2) = (74.6, 4) and (E1, t1) = (70.8, 0).

m = (74.6 - 70.8) / (4 - 0)
m = 3.8 / 4
m = 0.95

Y-Intercept (b):
To find the y-intercept (b), we can substitute the values from one of the points (E, t) into the slope-intercept form (y = mx + b) and solve for "b".

Let's use the point (70.8, 0):
70.8 = 0.95(0) + b
70.8 = b

The value of "b" is 70.8.

Now we have the slope (m = 0.95) and the y-intercept (b = 70.8).

Therefore, the linear function that fits the data is:
E(t) = 0.95t + 70.8

(Rounded to the nearest tenth)
E(t) = 0.9t + 70.8