Question

A salesperson makes a base salary of $2000 per month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.

Write and graph the piecewise-defined function to represent the salary.

Answer 1

The piece-wise modeled function to represents the salary(in $) is:

`f(x)=\begin{cases}2,000 & \text{ if } x\leq 40,000 \\ 2000+0.05(x-40000)& \text{ if } x>40,000 \end{cases}`

Explanation:

Given the statement: A salesperson makes a base salary of $2000 per month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.

Let x represents the amount of sales and

f(x) represents the salary of salesperson.

From the given statement this implies that till the sale of $40,000, the salary of a salesperson is remains constant i.e $2000

f(x) =2000 when
`x\leq 40,000`

Now, a salesperson earns an additional of 5% on the amount in sales over $40,000 i.e,

`f(x) = 2000+(5)/(100)(x-40000)` when
`x>40,000`

or

`f(x) = 2000+0.05(x-40000)` when
`x>40,000`

therefore, the piece-wise defined function to represents the salary is:

`f(x)=\begin{cases}2,000 & \text{ if } x\leq 40,000 \\ 2000+0.05(x-40000)& \text{ if } x>40,000 \end{cases}`

You can see the graph as shown below in the attachment: