Question

The percentage of soldiers who are unavailable for combat has increased approximately linear from 10% in 2007 to 17% in 2010. The main cause are due to repeated Deployments and health problems let P be the percentage of soldiers unavailable for combat at three years since 2000. find the equation of a linear model to describe the data

Answer 1

P = 0.0233t - 0.0633

Explanations:

The standard linear equation in point-slope form is expressed as;

`y-y_0=m(x-x_0)`

where:

• m is the ,slope, of the equation

,

• (x0, y0) is ,any point ,on the line

Let t be the number of years

Let P be the percentage of soldiers unavailable

This can be written in the coordinate form (t, P)

If the percentage of soldiers who are unavailable for combat has increased approximately linear from 10% in 2007 to 17% in 2010, the coordinate points on the line will be (7, 0.10) and (10, 0.17)

Determine the slope of the equation:

`\begin{gathered} m=(P_2-P_1)/(t_2-t_1) \\ m=(0.17-0.10)/(10-7) \\ m=(0.07)/(3) \\ m=0.0233 \end{gathered}`

Substitute any of the points and the slope into the expression below:

`\begin{gathered} P-P_0=m(t-t_0) \\ P-0.10=0.0233(t-7) \\ \end{gathered}`

Simplify to get the required linear equation:

`\begin{gathered} P-0.10=0.0233t-0.1633 \\ P=0.0233t-0.1633+0.10 \\ P=0.0233t_{}-0.0633 \end{gathered}`

Hence the equation of a linear model to describe the data is P = 0.0233t - 0.0633