In 1990, the life expectancy of males in a certain country was 62.1 years, it was 65.3 years. Let E represent life expectancy in year T and let t represent the number of years since 1990.
What is the subject? What is the question?
To find the equation that relates the life expectancy (E) to the number of years since 1990 (t), we need to consider the given information.
Given that in 1990, the life expectancy of males in a certain country was 62.1 years, we can use this as a starting point. Since 1990 is the reference year, the number of years since 1990 (t) would be 0 in that year. So, when t = 0, E = 62.1.
Given that in 1993, the life expectancy was 65.3 years, we can use this as another data point. The number of years since 1990 in 1993 would be 1993 - 1990 = 3. So, when t = 3, E = 65.3.
Now, we have two data points: (0, 62.1) and (3, 65.3). We can use these points to find the equation of a linear relationship between E (life expectancy) and t (the number of years since 1990).
Step 1: Calculate the slope (m) using the formula:
m = (E2 - E1) / (t2 - t1)
= (65.3 - 62.1) / (3 - 0)
= 3.2 / 3
= 1.0667
Step 2: Plug in the slope and one of the data points (e.g., (0, 62.1)) into the point-slope form equation:
E - E1 = m(t - t1)
E - 62.1 = 1.0667(t - 0)
E - 62.1 = 1.0667t
Step 3: Simplify the equation:
E = 1.0667t + 62.1
Therefore, the equation that relates the life expectancy (E) to the number of years since 1990 (t) is E = 1.0667t + 62.1.