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

Answer:

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

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

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 $x\leq 40,000$

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

$f(x) = 2000+\frac{5}{100}(x-40000)$  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: