Question

If Pam works more than $40$ hours per week, her hourly wage for every hour over $40$ is $1.5$ times her normal hourly wage of $\$7$.

Write a piecewise-defined function that gives Pam's weekly pay $P\left(h\right)$ in terms of the number of hours $h$ that she works.

Answer 1

Write a piecewise-defined function:

Given data,

Hours worked is smaller than or equal to $40$ (no overtime). this can be expressed as,

$h\le 40$

Hours worked is larger than $40$ (overtime). this can be expressed as,

$h>40$

Let, Pam's weekly wages is $P\left(h\right)$

Worked hours is $h$

The pay $P\left(h\right)$, in dollars , while a given condition is true. this can be expressed as,

$P\left(h\right)=7h$

Then, for the first hours of the work at $h=40$ then the above equation becomes,

$$\begin{gathered} P\left(h\right)=7\times 40 \\ P\left(h\right)=280 \end{gathered}$$

The normal rate can be expressed as,

$1.5\times \$7=10.5$

And the $\left(h-40\right)$ is for every hours over $40$

Then the we can express the function as,

$$\begin{gathered} P\left(h\right)=7h\left[\text{when}h\le 40\right] \\ P\left(h\right)=280+12\left(h-40\right)\left[\text{when}h>40\right] \end{gathered}$$

Hence, piecewise-defined function is shown.