Question

Between 1900 and 2003, the life expectancy for men and women in the United States increased dramatically. For men, life expectancy increased from 48 to 75 years. For women, life expectancy increased from 51 to 80 years.† Model male life expectancy M as a function of female life expectancy f. (Round your coefficients to two decimal places.)

Answer 1

`M(f)=0.93f+0.52`

Explanation:

Our goal is to obtain the "male life expectancy" (called 'M') as a function of "female life expectancy" (called 'f'). As it's given only two points, we asume a linear function:
`M(f)=\alpha f + M_o`. Where
`\alpha` is the pendent and
`M_o` is the intercept.

So, we have to find
`\alpha` and
`M_o` for the two given points: 1900 (
`f = 51`and 2003 (
`f=80`).

`M(51)=51\alpha + M_o=48\\\\M(80)=80\alpha + M_o=75\\\\M(80)-M(51)=\alpha(80-51)=75-48\\29\alpha=27 \Rightarrow \alpha = 27/29 = 0.93\\\\M(80) = 0.93(80) + M_o = 75\\74.48 + M_o = 75\\\\\Rightarrow M_o = 75 - 74.48 = 0.52`

In conclusion, getting
`\alpha = 0.93` and
`M_o = 0.52`, our function results:
`M(f) = 0.93f+0.52`.