Is This Piecewise Function for Sales Commission Correct?

[939]

Homework Statement

Make a piecewise function. If possible, please check my work.

- Salesperson has salary of $500.
- On first 10 000 of sales, earns 10% commission.
- On next 10 000 of sales, earns 20% commission.
- Earns 25% commission on any additional sales.

(note: didn't simplify to show where I got the numbers)

2. The attempt at a solution

500 + 0.10(x), x ≤ 10 000

500 + 0.10(10 000) + 0.20(x - 10 000), 10 000 < x ≤ 20 000

500 + 0.10(10 000) + 0.20(20 000) + 0.25(x), x > 20 000

 

[Mark44]

Homework Statement

Make a piecewise function. If possible, please check my work.

- Salesperson has salary of $500.
- On first 10 000 of sales, earns 10% commission.
- On next 10 000 of sales, earns 20% commission.
- Earns 25% commission on any additional sales.

(note: didn't simplify to show where I got the numbers)

2. The attempt at a solution

500 + 0.10(x), x ≤ 10 000

500 + 0.10(10 000) + 0.20(x - 10 000), 10 000 < x ≤ 20 000

500 + 0.10(10 000) + 0.20(20 000) + 0.25(x), x > 20 000

The last line has an error. The saleman earns a 25% commission on "any additional sales." That means any sales over $20,000.

 

[939]

The last line has an error. The saleman earns a 25% commission on "any additional sales." That means any sales over $20,000.

Thanks! But doesn't x > 20 000 show that sales must be over 20 000? (i.e. in the function, you would only multiply x by 0.25 if sales, x, were over 20 000)

 

[haruspex]

Thanks! But doesn't x > 20 000 show that sales must be over 20 000? (i.e. in the function, you would only multiply x by 0.25 if sales, x, were over 20 000)

Yes, the sales are over 20,000, but the 25% commission is only on the excess over 20,000.
You did it correctly in the middle line: ..., 0.20(x - 10 000), ...