In 1992, the life expectancy of males in a certain country was72.7 years. In 199

Question

In 1992, the life expectancy of males in a certain country was72.7 years. In 1997, it was 76.4 years. Let E represent the lifeexpectancy in year t and let t represent number of years since1992. The linear function E(t) that fits the data is E(t)= ?t + ? Use the function to predict the life expectancy of males in2007. E(15)= ? In 1992, the life expectancy of males in a certain country was72.7 years. In 1997, it was 76.4 years. Let E represent the lifeexpectancy in year t and let t represent number of years since1992. The linear function E(t) that fits the data is E(t)= ?t + ? Use the function to predict the life expectancy of males in2007. E(15)= ?

Explanation / Answer

The keywords to this problem are "let t represent number ofyears since 1992". This means that 1992 is going to beyour baseline, and your starting value. So your equation shouldproduce 72.7 at 0 years, because in 1992( the starting point), thelife expectancy of males in a certain country was 72.7 years. So, your data consists of: 0 years = 72.7 5 years (1997, because it is five years from 1992)= 76.4 Therefore, we know that E(t)= ?t + 72.7, because 72.7is your starting point. To find the rate at which the lifeexpectancy rises, we need to subtract 72.7 from 76.4. So76.4-72.7=3.7 This tells us that the life expectancy grew 3.7 overfive years. Then we need to divide 3.7 by 5, because it is the rateover five years. So, 3.7/5=.74 therefore .74 is your mystery numberthat fills in the question mark. So, E(t)= .74t + 72.7 We can test this using t=0 to represent 1992. E(0)=.74(0) + 72.7E(0)=72.7 so the life expectancy is 72.7 in 1992. We can also test this using t=5 to represent 1997. E(5)=.74(5) +72.7 E(5)=3.7 + 72.7 E(5)= 76.4 so the life expectancy is 76.4 in 1997. Use the function to predict the life expectancy of males in2007. E(15)= ? 2007 is 15 years from 1992, therefore t=15. E(15)= .74(15) + 72.7 E(15)= 11.1 + 72.7 E(15)= 83.8 therefore the life expectancy of males in 2007 is83.8

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