Question

The life expectancy for females in a certain country born during 1980−1985 was approximately 75.2 years. This grew to 76 years during 1985−1990 and to 76.2 years during 1990−1995. Construct a model for this data by finding a quadratic equation whose graph passes through the points ​(0,75.2​),​(5​,76​),and ​(10​,76.2​). Use this model to estimate the life expectancy for females born between 1995 and 2000 and for those born between 2000 and 2005.

Let x be the number of years since 1980 and y be the life expectancy for a person born between ​(1980+​x) and

​(1980+x+​5). Find a quadratic equation whose graph passes through the points ​(0,75.2​), ​(5​,76​), and ​(10​,76.2​).

Y=?

According to the model, the life expectancy of a female born between 1995 and 2000 in this country is ___?_ years.

According to the model, the life expectancy of a female born between 2000 and 2005 in this country is __?__ years.

Answer 1

Let x be the number of years since 1980 and y be the life expectancy for a person born between ​(1980+​x) and ​(1980+x+​5).

The quadratic equation that we want to estimate is

We have 3 data points and 3 unknowns.

the equation for ​(x=0,y=75.2​) is

the equation for ​(x=5,y=76​) is

the equation for ​(x=10,y=76.2​) is

Subtracting the last 2 we get

Lastly we get the value of b using

the quadratic equation which passes through the points ​(0,75.2​), ​(5​,76​), and ​(10​,76.2​) is

Ans:

The years 1995 and 2000 is (1980+15) and (1980+15+5)

That means x=15 for the years 1995 and 2000. Substituting x=15 in the equation we get

Ans: According to the model, the life expectancy of a female born between 1995 and 2000 in this country is 75.8 years

The years 2000 and 2005 is (1980+20) and (1980+20+5)

That means x=20 for the years 2000 and 2005. Substituting x=20 in the equation we get

Ans: According to the model, the the life expectancy of a female born between 2000 and 2005 in this country is 74.8 years