Carter cadillac pays commission to its car sales staff. They are paid a percent of the profit the dealership makes on the car, not on selling price of the car. If the profit is less than or equal to $500, the commission rate is 18%. If the profit is greater than $500 and less than or equal to $2000, the commission rate is 24% of the profit. If the profit is above $2000, the rate 27% of the profit. If p represents the profit, express the commission c(p) algebraically as a split function.

Answer:[tex]c(p)=\left \{ {{0.18p} \ \ When \ p \leq 500\\\atop {{0.24p} \ \ When 500<p \leq 2000\\\atop {{0.27p} \ \ When p>2000\right[/tex]Step-by-step explanation:From the 3 statements given, we can say:The commission is 18% of p, when p is LESS THAN OR EQUAL TO 500The commission is 24% of p, when 500 < p ≤ 2000The commission is 27% of p, when p is GREATER THAN 2000This can be written as a piecewise function (split function) of the form shown below:[tex]c(p)=\left \{ {{0.18p} \ \ When \ p \leq 500\\\atop {{0.24p} \ \ When 500<p \leq 2000\\\atop {{0.27p} \ \ When p>2000\right[/tex]