Anthony sells cars. Each month, he is paid $2,000, plus a $15\%$ commission on monthly sales above $20,000. Which function calculates his monthly earnings $(E)$ as a function of $m$ his monthly sales?
$E(m)=2,000+0.15(m-20,000)$
$E(m)=2,000+0.15(m+20,000)$
$E(m)=2,000+15(m-20,000)$
$E(m)=2,000+15(m+20,000)$
Answer (1)
The problem states that Anthony earns $2 , 000 plus a 15% commission on sales above $20 , 000 .
Define m as monthly sales and E ( m ) as monthly earnings.
Calculate the commission as 0.15 ( m − 20 , 000 ) when 20,000"> m > 20 , 000 .
Express the total earnings as E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 ) .
The function that calculates Anthony's monthly earnings is E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 ) .
Explanation
Problem Analysis Let's analyze the problem. Anthony receives a base salary of $2 , 000 and a commission of 15% on sales exceeding $20 , 000 . We need to determine the function E ( m ) that represents his total monthly earnings based on his monthly sales m .
Calculating Earnings If Anthony's monthly sales m are greater than $20 , 000 , his commission is calculated as 15% of the amount exceeding $20 , 000 , which is 0.15 ( m − 20 , 000 ) . His total earnings E ( m ) would then be his base salary plus his commission: E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 ) .
Considering Sales Above 20 , 000 I f A n t h o n y ′ s m o n t h l ys a l es m a re l ess t han ore q u a lt o $20,000 , h eo n l yrece i v es hi s ba ses a l a ryo f $2,000 . Ho w e v er , t h e q u es t i o nim pl i es t ha tw e a re l oo kin g f or a s in g l e f u n c t i o n t ha t a ppl i es w h e n m > 20,000$.
Final Function Therefore, the function that calculates Anthony's monthly earnings E ( m ) as a function of his monthly sales m is E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 ) .
Examples
Understanding commission-based earnings can help you plan your finances. For example, if you are a salesperson, knowing how your earnings are calculated can motivate you to reach higher sales targets. By understanding the formula E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 ) , you can estimate your potential income based on your sales performance and set realistic financial goals. This can also help you in negotiating better compensation packages or evaluating job offers.
