A business banker works on commission based on the amount of loans made. He

earns 5% on all loans made below $5000. He then begins earning 10% commission

until he hits $50,000 in loans. Beginning with $50,000 his commision jumps to 15% for

all remaining loans. Find a piecewise function for the banker's commission on the total loans of x dollars.

Question

Cecilia Everett

Mathematics

2 April, 04:25

A business banker works on commission based on the amount of loans made. He

earns 5% on all loans made below $5000. He then begins earning 10% commission

until he hits $50,000 in loans. Beginning with $50,000 his commision jumps to 15% for

all remaining loans. Find a piecewise function for the banker's commission on the total loans of x dollars.

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Answers (1)

Know the Answer?

Ivy Pineda · Answer 1

Step-by-step explanation:

Well first let's see what they would look like if they weren't piecewise.

If all commissions were 5%, and we say the loan amount is x, the commission then is. 05x. Similarly, 10% is. 1x and 15% is. 15x Now we just need to incorporate these into a piecewise form.

We are breaking up the piecewise function into what x is. the three groups are $0-$4,999, $5,000-49,999 and $50,000 and higher. So basically we just write this out.

We will have to put these in terms of inequalities so 0 ≤ x ≤ 4,999, 5,000 ≤ x ≤ 49,999 and 50,000 ≤ x Now! we're set.

basically you're just going to list these off like f (x) =.05x when 0 ≤ x ≤ 4,999 and similarly list the other two. Do you know how it is supposed to look?