Question

a sales person makes a base salary of $300 per week plus 13% commission on sales.
(a) write a linear function to model the sales person’s weekly salary ( s(x) ) for ( x ) dollars in sales.
(b) evaluate ( s(8000) ) and interpret the meaning in the context of this problem.
part 1 of 2
(a) the linear function is ( s(x) = 300 + 0.13x ) for ( x geq 0 ).
part: 1 / 2
part 2 of 2
(b) ( s(8000) = 1340 ) means that the sales person will make $ if $ in merchandise is sold for the week.

Explanation:

Step1: Define linear salary function

Base salary is fixed, commission is 13% of sales $x$.
$S(x) = 300 + 0.13x$ for $x\geq0$

Step2: Substitute $x=8000$ into function

Calculate commission first, then add base salary.
$S(8000) = 300 + 0.13\times8000$

Step3: Compute the total salary

Calculate the product then sum.
$S(8000) = 300 + 1040 = 1340$

Answer:

(a) $S(x) = 300 + 0.13x$ for $x\geq0$
(b) $S(8000)=1340$ means that the sales person will make $\$1340$ if $\$8000$ in merchandise is sold for the week.