in 1990, the life expectancy of males in a certain country was 68.1 years. in 1995, it was 70.9 years. let E represent the life expectancy in year t and let t represent the number of years since 1990

F(x)=

To find the function that represents the life expectancy (E) in year t, we can use the given information. We are given the life expectancy in two different years, 1990 and 1995, and we need to determine the relationship between the life expectancy and the number of years since 1990.

Let's start by finding the difference in life expectancy between the two years.

The life expectancy in 1995 (E) is 70.9 years, and in 1990 (E) it was 68.1 years. So, the difference in life expectancy is:

ΔE = E₁ - E₀ = 70.9 - 68.1 = 2.8

Now, let's find the difference in years between the two years.

The number of years since 1990 in 1995 (t) is 1995 - 1990 = 5.

Now, we have the change in life expectancy (ΔE) and the change in years (Δt). To find the relationship between E and t, we can use the formula for the slope of a linear function:

slope (m) = ΔE / Δt

m = 2.8 / 5 = 0.56

The slope of the linear function representing the life expectancy is 0.56.

Now, we can find the equation of the line using the slope-intercept form:

E = mt + b

where m is the slope and b is the y-intercept.

To find the value of b, we can use one of the points we have. Let's use the point (1990, 68.1) since it represents the starting point.

Using the values, we have:

68.1 = 0.56 * 0 + b

Now, we can solve for b:

b = 68.1

So, the equation representing the life expectancy (E) in year t is:

E(t) = 0.56t + 68.1.

Therefore, F(x) = 0.56x + 68.1.