Question

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 1

Answer:

The piecewise-defined function to model the salesperson's total monthly salary (in $) is,

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

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.

$f(x)=2000$    for   $x\leq 40,000$

He will get commision of 5% on the amount in sales over $40,000.

$f(x)=2000+\frac{5}{100}(x-40000)$  for  $x>40,000$

Therefore the piecewise-defined function to model the salesperson's total monthly salary (in $) is,

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

Answer 2

The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis $\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{ if }}x \leqslant 40000 \hfill\\2000 + 0.05\left( {x - 40000} \right){\text{ if }}x > 40000 \hfill\\\end{gathered}\right.}$.

Further explanation:

The piecewise defined function is defined as a function that takes different values in different interval. It is defined on the sequence of intervals.

Given:

The base salary is $\ 2000$.

He will earn $5\%$ additional commission on the amount sales over $\ 40000$.

Explanation:

The base salary of a salesperson in a month is $2000.

If the salesperson reaches to $40000, he will earns 5% additional commission on the amount sales over $\ 40000$.

The person get $\ 2000$ if sale less than  $\ 40000$.

$f\left( x \right) =2000{\text{ for }}x \leqslant 40000$.

The value of the function for less than $40000 is  $f\left( x \right)=2000$.

If he sales over 40000 the amount he will get can be expressed as follows,

$f\left( x \right)=2000+\dfrac{5}{{100}}\left( {x - 40000} \right)$ for$x > 40000.$

The value of the function for greater than 40000 is  $f\left( x \right)=2000 + \dfrac{5}{{100}}\left({x - 40000} \right)$.

The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis $\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{if }}x \leqslant 40000\hfill\\2000 + 0.05\left( {x - 40000}\right){\text{if }}x > 40000 \hfill \\\end{gathered}\right.}$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear Equation

Keywords: solving equation, inverse operation, isolate, variable, addition property, good guess, solution, order of operations, reverse order, two solution, linear equation.