Question

How Long Will You Live? Many companies utilize life expectancy data to calculate items such as life insurance premiums or retirement benefits. The IRS is no exception. Use the data in the following table to answer the questions below. IRS Life Expectancy Table Current Age Expected Number of Additional Years to Live 35 47.3 40 42.5 1) The data given in the table is (approximately) linear. Using ordered pairs of the form (current age, number of additional years you are expected to live), find a linear function that fits the data for the ages given. Write your answer in slope-intercept form. y =__________________ 2) Graph the function on a separate sheet of graph paper and be sure to label the axes appropriately. Discuss the meaning of the slope and y-intercept. What do these numbers refer to in terms of life expectancy? The slope of line is ________________ and it means that … The y-intercept of the line is _________ and it means that … 3) Using the function you wrote in question 1, calculate the number of additional years that a 72 year-old person can expect to live. 4) What is the result of adding together the x- and y-coordinates of any ordered pair in this situation?

Answer 1

1) Let the linear equation be : y = mx+c.

By condition we have,

35m+c = 47.3..............(i)

40m+c = 42.5...............(ii)

Subtracting (i) from (ii) we get, 5m = -4.8 ,i.e., m = -4.8/5 ,i.e., m = -0.96

Putting this value in (ii) we get, 40*(-0.96)+c = 42.5

i.e., -38.4+c = 42.5

i.e., c = 80.9

Therefore, the linear equation is : y = -0.96x+80.9 ,i.e., y = 80.9-x (approx)

2) Graph of y = 80.9-x is :

Slope of the line is = -1.

This implies that the life expectancy is decreasing.

Y-intercept of the line is = 80.9

This implies that the maximum life expectancy is 80.9 years.

3) Given x = 72 years.

Then, y = 80.9-72 ,i.e., y = 8.9 years.

Therefore, the number of additional years that a 72 year-old person can expect to live is 8.9 years.

4) The result of adding together the x- and y-coordinates of any ordered pair in this situation is 80.9, which is the maximum life expectancy.