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Answer:
The answer is below
Step-by-step explanation:
The minimum payment on a credit card is based on the total amount owed. A credit card company uses the following rules: For a bill less than $20 the entire amount is due, for a bill of at least $20 but less than $500, the minimum due is $20. For a bill of at least $500 but less than $1000 the minimum due is $40 and for a bill of at least $1000 but less than $1500 the minimum due is $80 dollars. For a bill of $1500 or more the minimum due is 1/10th of the bill.
a. Write a function to describe the minimum payment due.
b. What is the minimum payment due if the bill is $345?
c. What is the minimum payment due if the bill is $1410?
d. What is the minimum payment due if the bill is $1700?
Solution:
Let B represent the minimum due payment for a bill in dollars and let x represent the bill in dollars. Therefore:
For x < 20, B = x
For 20 ≤ x < 500, B = 20
For 500 ≤ x < 1000, B = 40
For 1000 ≤ x < 1500, B = 80
For x ≥ 1500, B = (1/10)x
a)
[tex]B(x)=\left \{ {{x\ \ \ x<20} \atop {20\ \ 20\leq x<500\\\atop {40\ \ \ 500\leq x<1000\\\atop {80\ \ \ 1000\leq x<1500\\\atop {\frac{1}{10}x \ \ \ x>1500}}} }} \right.[/tex]
b) For 20 ≤ x < 500, B = 20
Therefore if the bill is $345 (x = 345), the minimum payment due would be $20
c) For 1000 ≤ x < 1500, B = 80
Therefore if the bill is $1410 (x = 1410), the minimum payment due would be $80
d) For x ≥ 1500, B = (1/10)x
Therefore if the bill is $1700 (x = 1700), the minimum payment due would be $170 (1/10 * 1700)