Question

An appliance vendor receives a base salary of $200 per week and a commission of 4% on all sales over $3,000 during the week. In addition, if the week's sales are $8,000 or more, the seller receives a $100 bonus. If x represents weekly dollar sales, express earnings E(x) as a function of x.

Answer 1

To express earnings E(x) as a function of x, consider the base salary, commission, and bonus. The earnings function accounts for the base salary, commission on sales over $3,000, and a bonus for sales $8,000 or more.

Step-by-step explanation:

To express earnings E(x) as a function of x, we need to consider the base salary, commission, and bonus. The base salary is $200 per week, which is a constant value. The commission is 4% of all sales over $3,000 during the week. So, if the weekly sales are x, the commission would be 4% of (x - 3000), which can be expressed as 0.04(x - 3000). The bonus is $100 if the weekly sales are $8,000 or more, so we can express the bonus as a piecewise function: 100 if x >= 8000, and 0 otherwise. Therefore, the earnings E(x) can be expressed as:

E(x) = 200 + 0.04(x - 3000) + 100 if x >= 8000

E(x) = 200 + 0.04(x - 3000) otherwise