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+ _
Use the formula below to predict the life expectancy of males in 2004
E (14) =
Life expectancy increases at a rate of (75.2-71.7)/4 = 3.5/4 = 0.875 yrs per yr.
E = 71.7 + 0.875 t
In 2004, t = 11 and E = 81.3
I doubt whether E can increase at that rate for very long, but that is what they want you to assume.
To begin solving this problem, we can start by identifying the given information and the formula provided.
Given:
- Life expectancy of males in 1993: 71.7 years
- Life expectancy of males in 1997: 75.2 years
Formula:
E(t) = _t + _
The formula represents the life expectancy (E) in years (t) since 1993. However, since the formula is incomplete, we need to determine the missing values.
To find the missing values, we can use the given information. We know that in 1993 (t = 0), the life expectancy was 71.7 years. This means that the term with the coefficient of t must be 71.7.
Next, we can use the information from 1997 (t = 4) where the life expectancy was 75.2 years. Plugging in these values into the formula, we have:
E(0) = 71.7
E(4) = 75.2
Substituting the values into the formula, we get:
71.7 = _0 + _
75.2 = _4 + _
From these equations, we can determine the missing values:
_0 + _ = 71.7 (Equation 1)
_4 + _ = 75.2 (Equation 2)
To find the missing values, we can subtract Equation 1 from Equation 2:
_4 + _ - (_0 + _) = 75.2 - 71.7
_4 - _0 + _ - _ = 3.5
Simplifying the equation, we can combine like terms:
3_ = 3.5
To isolate the term with the coefficient, we divide both sides by 3:
_ = 3.5/3
_ = 1.167
Now that we have the missing value, we can substitute it back into the formula:
E(t) = _t + _
E(t) = 1.167t + 1.167
Finally, to predict the life expectancy in 2004 (t = 14), we can plug in this value into the formula:
E(14) = 1.167(14) + 1.167
E(14) = 16.338 + 1.167
E(14) = 17.505
Therefore, the predicted life expectancy of males in 2004 is 17.505 years.