In 1990, the life expectancy of males in a certain country was 72.4 years. In 1994, it was 75.8 years...?

Let E represent the life expectancy in year t and let t represent the number of years since 1990.
The linear function E(t) that fits the data is
E(t)=__t + ___. (round to the nearest tenth)

Use the function to predict the life expenctancy of males in 2008.
E(18)=___. (round to the nearest tenth)

basically you are asked to find the linear function E(t)

given two points, (0,72.4) and (4,75.8)

slope = (75.8-72.4)/(4-0) = .85

so E(t) = .85t + b (compare with y = mx + b)
sub in (0,72.4) to solve for b

then evaluate E(18) by subbing in t = 18

To find the linear function E(t) that fits the data, we first need to determine the rate of change (slope) and the initial value (y-intercept) of the function.

Let's start by finding the slope of the function. The slope represents the rate at which the life expectancy is changing per year. We can calculate the slope by dividing the change in life expectancy by the change in years:

Slope = (final life expectancy - initial life expectancy) / (final year - initial year)

Given:
Initial life expectancy in 1990 = 72.4 years
Final life expectancy in 1994 = 75.8 years
Initial year = 1990
Final year = 1994

Slope = (75.8 - 72.4) / (1994 - 1990)
= 3.4 / 4
= 0.85

Next, let's find the y-intercept of the linear function. The y-intercept represents the value of life expectancy when t (the number of years since 1990) is zero. We can calculate the y-intercept by substituting the values of a known point (e.g., 1990) into the equation and solving for the y-intercept:

Using the known point (1990, 72.4):
E(t) = 0.85t + b
72.4 = 0.85(1990) + b
72.4 = 1691.5 + b
b = 72.4 - 1691.5
b = -1619.1

Now we have the values for the slope and y-intercept, we can write the linear function E(t) as follows:

E(t) = 0.85t - 1619.1

To predict the life expectancy in 2008 (18 years since 1990), we can substitute t = 18 into the function:

E(18) = 0.85(18) - 1619.1
= 15.3 - 1619.1
= -1603.8 (rounded to the nearest tenth)

Therefore, the predicted life expectancy of males in 2008 is approximately -1603.8 years (rounded to the nearest tenth). Note that a negative value doesn't make sense in this context, so it could be an indication that linear regression might not be the best fit for this particular dataset or that there might be some other factors affecting the life expectancy.