Question

Assume that the real-world context can be accurately modeled with a linear function.

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 female life expectancy F as a function of male life expectancy m. (Round your coefficients to two decimal places.)

Answer 1

`F=1.07m-0.56`

Explanation:

We are given that female life expectancy (F) can be modelled as a function of male life expectancy (m) with a linear function. Therefore:

• F represents the dependent variable (y-value).
• m represents the independent variable (x-value).

So, in terms of coordinates on a graph, (m, F) corresponds to (x, y).

For men (m), life expectancy increased from 48 to 75 years, and for women (F), life expectancy increased from 51 to 80 years.

Therefore, this gives us two (m, F) points:

• (48, 51)
• (75, 80)

To model female life expectancy (F) as a function of male life expectancy (m) with a linear function, we can use the equation of a straight line:

`\large\boxed{F = a \cdot m + b}`

where:

• F represents female life expectancy.
• m represents male life expectancy.
• a is the slope of the line.
• b is the y-intercept.

Calculate the slope (a) using the slope formula:

`\textsf{Slope}\;(a)=\frac{\textsf{Change in $F$}}{\textsf{Change in $m$}}=(80-51)/(75-48)=(29)/(27)=1.07\; \sf (2\;d.p.)`

Substitute the exact slope and one of the points (48, 51) into the equation and solve for b:

`51 = (29)/(27)(48) + b`

`b=51 - (29)/(27)(48)`

`b=51-(464)/(9)`

`b=-(5)/(9)`

`b=-0.56\; \sf (2\; d.p.)`

So, the linear function that models female life expectancy (F) as a function of male life expectancy (m) is:

`\large\boxed{\boxed{F=1.07m-0.56}}`