A salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000. Write a piecewise-defined function to model the salesperson's total monthly salary (in $) as a function

Answer:The piecewise-defined function to model the salesperson's total monthly salary (in $) is,[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]Step-by-step explanation:It is given that the salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.Let the x represents the amount of sales and f(x) represents the salary of salesperson.It means till the sale of $40,000, the salary of the salesperson is constant, i.e., $2000.[tex]f(x)=2000[/tex]    for   [tex]x\leq 40,000[/tex]He will get commision of 5% on the amount in sales over $40,000.[tex]f(x)=2000+\frac{5}{100}(x-40000)[/tex]  for  [tex]x>40,000[/tex]Therefore the piecewise-defined function to model the salesperson's total monthly salary (in $) is,[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]