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Over [174]
3 years ago
9

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

on on the amount in sales over $40,000.
Write and graph the piecewise-defined function to represent the salary.

Mathematics
1 answer:
hram777 [196]3 years ago
4 0

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:

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