Word Problems
Overview
Apply your understanding of functions to real-world situations. Learn to write functions from word problems and interpret function values in context.
Practice Problems
Question 1: A taxi charges $3 plus $2 per mile. Write a function for the cost C(m) where m is miles traveled. What is the cost for 7 miles?
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Answer: C(m) = 2m + 3; Cost for 7 miles = $17
C(7) = 2(7) + 3 = 14 + 3 = $17
Question 2: A pool is being filled at 50 gallons per minute. It already has 200 gallons. Write a function for the total water W(t) after t minutes. When will it have 700 gallons?
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Answer: W(t) = 50t + 200; It will have 700 gallons at t = 10 minutes
700 = 50t + 200, 500 = 50t, t = 10 minutes
Question 3: A gym membership costs $25 per month plus a $50 signup fee. Write a function for total cost C(m) after m months. How much will 12 months cost?
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Answer: C(m) = 25m + 50; 12 months costs $350
C(12) = 25(12) + 50 = 300 + 50 = $350
Question 4: The temperature starts at 68°F and drops 2°F every hour. Write a function T(h) and find the temperature after 5 hours.
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Answer: T(h) = 68 - 2h; After 5 hours: 58°F
T(5) = 68 - 2(5) = 68 - 10 = 58°F
Question 5: A phone plan costs $40 per month plus $0.05 per text. If the bill was $52.50, how many texts were sent?
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Answer: 250 texts
C(t) = 0.05t + 40. If 52.50 = 0.05t + 40, then 12.50 = 0.05t, t = 250 texts
Question 6: A candle is 12 inches tall and burns at 0.5 inches per hour. Write a function for height H(t) and find when it will be 3 inches tall.
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Answer: H(t) = 12 - 0.5t; It will be 3 inches after 18 hours
3 = 12 - 0.5t, -9 = -0.5t, t = 18 hours
Question 7: A streaming service has 5 million subscribers and gains 200,000 per month. Write a function S(m) for subscribers after m months. How many after 6 months?
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Answer: S(m) = 200,000m + 5,000,000; After 6 months: 6,200,000 subscribers
S(6) = 200,000(6) + 5,000,000 = 1,200,000 + 5,000,000 = 6,200,000
Question 8: A car rental costs $35 per day plus $0.20 per mile. If the total cost was $79 for one day, how many miles were driven?
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Answer: 220 miles
C(m) = 0.20m + 35. If 79 = 0.20m + 35, then 44 = 0.20m, m = 220 miles
Question 9: Water drains from a tank at 15 gallons per minute. The tank starts with 450 gallons. Write a function and determine when it will be empty.
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Answer: W(t) = 450 - 15t; Empty after 30 minutes
0 = 450 - 15t, 15t = 450, t = 30 minutes
Question 10: A savings account starts with $500 and earns $15 per month in interest. Write a function B(m) and find the balance after 2 years.
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Answer: B(m) = 15m + 500; After 2 years (24 months): $860
B(24) = 15(24) + 500 = 360 + 500 = $860