In 1995, the life expectancy of males in a certain country was 64.8 years. In 1999, it was 67.2 years. Let E represent the life ecpectancy in year t and let t represent the number of years since 1995.
E(t)= t+ (round to nearest tenth
Use the function to predict the life expectancy of males in 2006. E(11)=
(round to nearest tenth)
In 1995--64.8 yrs
In 1999--67.2 yrs
To write the equation, use the points
1999 - 1995 = 4 yrs
1995--(0, 64.8)
1999--(4, 67.2)
Equation through two points,
y - y1 = (y2 - y1)/(x2 - x1) * (x - x1)
y - 64.8 = (67.2 - 64.8)/(4 - 0) * (x-0)
y - 64.8 = 2.4/4 x
y - 64.8 = 0.6x
y = 0.6x + 64.8
Since, the function should be E(t),
E(t) = 0.6t + 64.8
To find E(t) for 2006,
E(11) = 0.6(11) + 64.8
E(11) = ?
Thank you so much for the help. Although still slightly confused I now have something to work with to figure out what I am doing. I have had such a difficult time with this class. If it wasn't for all of you guys I would be lost. Thanks again
To solve this problem, we can use the given information to find the equation for the relationship between life expectancy and the number of years since 1995.
First, we can define the initial year as t=0 (1995) and the life expectancy as E(0)=64.8 years.
In 1999, the life expectancy was E(4)=67.2 years, which means that after 4 years (from t=0 to t=4), the life expectancy increased by 67.2 - 64.8 = 2.4 years.
Based on this information, we can conclude that the life expectancy increases at a constant rate of 2.4 years per 4 years. To find how much the life expectancy increases per year, we divide the increase by the number of years: 2.4/4 = 0.6 years per year.
Now we can write the equation for life expectancy E(t) in terms of the number of years t since 1995:
E(t) = 64.8 + 0.6t
To predict the life expectancy for 2006, we need to find the value of t when t=11 years.
E(11) = 64.8 + 0.6(11)
E(11) = 64.8 + 6.6
E(11) = 71.4 years
Therefore, using the function E(t) = 64.8 + 0.6t, we can predict that the life expectancy of males in 2006 would be 71.4 years (rounded to the nearest tenth).
To predict the life expectancy of males in 2006 using the given function, we need to substitute t = 11 into the equation E(t) = t + 64.8.
E(11) = 11 + 64.8
E(11) = 75.8
Therefore, the predicted life expectancy of males in 2006 is 75.8 years.