Piecewise Functions Word Problems

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 52 hour week?

• $520

• $708

• $840

• He works for free!

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

• $1020

• $1140

• $840

• He works for free!

How much does it cost to rent the Karaoke machine for 3 days?

• $50
• $100
• $150
• $175

If you have $75, how many days can you rent the Karaoke machine?

• 0 days
• 1 day
• 2 days
• 3 days

How much does it cost to make 300 photocopies?

• $24.00
• $20.00
• $40.00
• $300.00

Does it cost to more to make 500 or 550 photocopies?

• 500 photocopies cost more

• 550 photocopies cost more

• It costs the same

• $35.00

• $12.75
• $35
• $45
• $27.75

• $12.75
• $35
• $43.40
• $27.75

When a diabetic takes long-acting insulin, the insulin reaches its peak effect on the blood sugar level in about three hours. This effect remains fairly constant for 5 hours, then declines, and is very low until the next injection. In a typical patient, the level of insulin might be modeled by the function pictured here.

f(t) represents the blood sugar level at time t hours after the time of the injection. If a patient takes insulin at 6 am, find the blood sugar level at 3pm.

• 220

• 160

• 140

• 60

For a cellular phone billing plan, $50 per month buys 400 minutes or less. Additional time costs $0.30 per minute. Let the monthly cost C(x) be a function of the time x.

Which piecewise function represents this situation?

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