In 1195 the life expectancy of males in a certain country was 66.5 years. In 1999 it was 69.1 years. Let E rep. the life expectancy in years t and let t rep. the number of years since 1995
To find the life expectancy in years t, we can use the equation E = mt + b, where E represents the life expectancy, t represents the number of years since 1995, m represents the rate of change, and b represents the initial life expectancy in 1995.
Given that the life expectancy in 1995 was 66.5 years and the life expectancy in 1999 was 69.1 years, we can use the values (t₁, E₁) = (0, 66.5) and (t₂, E₂) = (4, 69.1) to find the values of m and b.
First, calculate the rate of change, m:
m = (E₂ - E₁) / (t₂ - t₁)
= (69.1 - 66.5) / (4 - 0)
= 2.6 / 4
= 0.65
Second, calculate the initial life expectancy in 1995, b:
b = E₁ - mt₁
= 66.5 - 0.65 * 0
= 66.5
Now we can substitute the values of m and b into the equation E = mt + b to get the life expectancy in years t:
E = 0.65t + 66.5
This equation represents the relationship between the number of years since 1995 (t) and the life expectancy (E) in the given country.