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3. A salesperson makes a base salary of $2100 per month. Once he reaches $42000 in total sales, he earns an additional 5% comission on the amount of sales over $42000.

a. (2 points) Write a piecewise-defined function to model the salesperson’s total monthly salary S(x) (indollars) as a function of the amount of sales x.

b. (2 points) Graph the function. Indicate the numerical scale on the horizontal and vertical axes of
your graph, and indicate which axis represents the salary and which is the sales.

c. (1 point) If the salesperson had $80000 in sales, how much was his salary for that month?

d. (2 points) If the salesperson’s total salary for a month was $4500, how much were his total sales for
that month?

e. (2 points) Compute S(25000) and interpret what this means in the context of the problem (in terms of
the monthly salary and the sales)

Answer :

Answer:

The piecewise-defined function to model the salesperson's total monthly salary (in $) is,

f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}

Step-by-step explanation:It is given that the salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.

Let the x represents the amount of sales and f(x) represents the salary of salesperson.

It means till the sale of $40,000, the salary of the salesperson is constant, i.e., $2000.

   for  

He will get commision of 5% on the amount in sales over $40,000.

 for  

Therefore the piecewise-defined function to model the salesperson's total monthly salary (in $) is,

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