In 1995, life expectancy of males in a certain country was 72.6 years. In 2000, it was 76.1 years. Let E represent life expectancy in year t and let t the number of years since 1995.
E=((76.1-72.6)/5) * t + 72.5
To find the equation for life expectancy as a function of the number of years since 1995, we can use the information given about life expectancy in 1995 and 2000.
Let's start by assigning variables:
- E: Life expectancy in year t
- t: Number of years since 1995
According to the data, in 1995 (when t = 0), the life expectancy is 72.6 years. We can use this information to find the initial value of E, which we can call E0.
E0 = 72.6
In 2000 (when t = 5), the life expectancy is 76.1 years. We can use this information to find the rate of change of E over time. Let's call this rate of change m.
E5 = 76.1
Using the formula for a linear equation, we can write the equation as:
E = mt + b
Since we have two points (0, 72.6) and (5, 76.1), we can substitute these values into the equation to find the equation that describes the relationship between E and t.
When t = 0, E = 72.6:
72.6 = m(0) + b
72.6 = b
When t = 5, E = 76.1:
76.1 = m(5) + 72.6
Substituting b = 72.6 into the equation above:
76.1 = 5m + 72.6
Rearranging the equation:
5m = 76.1 - 72.6
5m = 3.5
Dividing both sides by 5:
m = 3.5 / 5
m = 0.7
Now, we have the values of m and b, so we can write the equation for life expectancy as a function of the number of years since 1995:
E = 0.7t + 72.6
Using this equation, you can now calculate the life expectancy for any year since 1995.