Answer:
The piece-wise modeled function to represents the salary(in $) is:
[tex]f(x)=\begin{cases}2,000 & \text{ if } x\leq 40,000 \\ 2000+0.05(x-40000)& \text{ if } x>40,000 \end{cases}[/tex]
Step-by-step 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 [tex]x\leq 40,000[/tex]
Now, a salesperson earns an additional of 5% on the amount in sales over $40,000 i.e,
[tex]f(x) = 2000+\frac{5}{100}(x-40000)[/tex] when [tex]x>40,000[/tex]
or
[tex]f(x) = 2000+0.05(x-40000)[/tex] when [tex]x>40,000[/tex]
therefore, the piece-wise defined function to represents the salary is:
[tex]f(x)=\begin{cases}2,000 & \text{ if } x\leq 40,000 \\ 2000+0.05(x-40000)& \text{ if } x>40,000 \end{cases}[/tex]
You can see the graph as shown below in the attachment:
