I am lost, and I bet it is simple, but I have been working with many problems and I keep coming back to this and I grow increasingly confused. How do I begin to solve this problem?
In 1993 the life expectancy of males in a certain country was 71.7 years. In 1997 it was 75.2 years. Let E represent the life expectancy in years t and let t represent the number of years since 1993
E(t)=_t+ _
E (14) =
Answered elsewhere, following a repeated post
To solve this problem, we can use a linear equation to represent the life expectancy over time. In this case, the equation will be in the form: E(t) = mt + b, where E(t) represents the life expectancy in years at time t, m represents the rate of change in life expectancy per year, and b represents the initial life expectancy in the base year.
Here we are given the life expectancy in 1993 (t=0) as 71.7 years and in 1997 (t=4) as 75.2 years. We can use these two data points to find the values of m and b.
First, we need to find the rate of change (m). We can do this by calculating the difference in life expectancy between 1993 and 1997, and dividing it by the difference in time (4 years).
Change in life expectancy = 75.2 - 71.7 = 3.5 years
Change in time = 4 - 0 = 4 years
Rate of change (m) = Change in life expectancy / Change in time = 3.5 / 4 = 0.875
Now, we can use the value of m to find the initial life expectancy (b). We can substitute one of the given data points into the equation and solve for b.
Using the data point (1993, 71.7):
E(t=0) = 0.875 * 0 + b
71.7 = b
So, b = 71.7
Now we have the values of m and b:
m = 0.875
b = 71.7
Now we can substitute these values into the equation:
E(t) = 0.875t + 71.7
To find E(14), we substitute t = 14 into the equation:
E(14) = 0.875 * 14 + 71.7
E(14) = 12.25 + 71.7
E(14) ≈ 83.95
Therefore, the life expectancy in the country in the year 2007 (14 years after 1993) is approximately 83.95 years.