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70 POINTS PLEASE HELP
A sales person makes a base salary of $400 per week plus 13% commission on sales.
1) write a linear function to model the sale persons weekly salary s(x) for x dollars in sales
Please review the picture for part 2

70 POINTS PLEASE HELP A sales person makes a base salary of 400 per week plus 13 commission on sales 1 write a linear function to model the sale persons weekly class=

Respuesta :

To model the salesperson's weekly salary \( s(x) \) for \( x \) dollars in sales, we need to consider the base salary plus the commission earned on sales. The commission earned is calculated as 13% of the total sales \( x \).

So, the linear function \( s(x) \) can be expressed as:

\[ s(x) = \text{Base Salary} + \text{Commission} \]

\[ s(x) = 400 + 0.13x \]

Where:

- \( s(x) \) is the weekly salary (in dollars).

- \( x \) is the total sales (in dollars).

- \( 400 \) is the base salary (in dollars per week).

- \( 0.13x \) is the commission earned (in dollars), which is 13% of the total sales \( x \).

This linear function represents the relationship between the salesperson's weekly salary and the amount of sales made.

msm555

Answer:

1) Linear function: [tex]\sf S(x) = \$400 + 0.13x [/tex]

2) [tex]\sf S(\$8000) =\$ 1440 [/tex]

Step-by-step explanation:

(a) To model the sales person's weekly salary [tex]\bold{\sf S(x)}[/tex] based on sales [tex]\bold{\sf x}[/tex], we can use the following linear function:

[tex]\sf S(x) = \$400 + 13\%\textsf{ of x} [/tex]

[tex]\sf S(x) = \$400 + 0.13x [/tex]

In this function:

- [tex]\bold{\sf \$400}[/tex] represents the base salary per week.

  • - [tex]\bold{\sf 0.13x}[/tex] represents the commission earned based on sales [tex]\bold{\sf x}[/tex],
  • where [tex]\bold{\sf 0.13}[/tex] (or [tex]\bold{\sf 13\%}[/tex]) is the commission rate.

Therefore, [tex]\bold{\sf S(x)}[/tex] gives the total weekly salary for a given amount of sales [tex]\bold{\sf x}[/tex].

(b) To evaluate [tex]\bold{\sf S(\$8000)}[/tex], substitute [tex]\bold{\sf \$8000}[/tex] for [tex]\bold{\sf x}[/tex] in the function [tex]\bold{\sf S(x)}[/tex]:

[tex]\sf S(\$ 8000) = \$400 + 0.13(\$8000) [/tex]

[tex]\sf S(\$ 8000) = \$ 400 +\$ 1040 [/tex]

[tex]\sf S(\$ 8000) = \$ 1440 [/tex]

Interpretation:

When [tex]\bold{\sf x = \$ 8000}[/tex] dollars in sales, the sales person's weekly salary [tex]\bold{\sf S(8000)}[/tex] will be [tex]\bold{\sf 1440}[/tex] dollars. This total includes the base salary of [tex]\bold{\sf 400}[/tex] dollars per week plus [tex]\bold{\sf 13\%}[/tex] commission on sales, which amounts to [tex]\bold{\sf 1040}[/tex] dollars ([tex]\bold{\sf 0.13 \times 8000}[/tex]) for the week.