in 2000 the life expectancy of males born in that year was 74.3 years. in 2010 i
ID: 3034816 • Letter: I
Question
in 2000 the life expectancy of males born in that year was 74.3 years. in 2010 it was 76.2 years let e(t) represent life expectancy and t the number of years since 2000. predict life expectancy for males in 2020 in 2000 the life expectancy of males born in that year was 74.3 years. in 2010 it was 76.2 years let e(t) represent life expectancy and t the number of years since 2000. predict life expectancy for males in 2020 in 2000 the life expectancy of males born in that year was 74.3 years. in 2010 it was 76.2 years let e(t) represent life expectancy and t the number of years since 2000. predict life expectancy for males in 2020Explanation / Answer
In our question it is not mentioned if the increase in population is a linear function or exponential. We assume it to be a linear function E(t) of time ‘t’.
We know that the graph of a linear function is a straight line and the equation of a straight line between any two points (x1,y1) and (x2,y2) is given by:
y - y1 = {(y2-y1)/(x2-x1)}* (x - x1)
In our question, there are two ordered pairs given : (2000, 74.3), and (2010, 76.2).
Now since ‘t’ is the time in years since year 2000 so we convert the data in terms of years like : (0, 74.3) and (10, 76.2).
Now we treat these two ordered pairs as the two points…
Thus, we have from above linear equation for a straight line,
y - 74.3 = {(76.2 - 74.3)/(10 - 0)}* (x - 0)
or y - 74.3 = (1.9 / 10) * x
or y = 74.3 + 0.19 * x
We have the function is E(t), where x = t and y = E(t), so we have
E(t) = 74.3 + 0.19*t [t = number of years since year 2000]
Now we can find the required prediction of life expectancy for males in year 2020 easily like below:
t = 2020 – 2000 = 20
E(20) = 74.3 + 0.19 * 20
= 74.3 + 3.8
= 78.1
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