NBT NBT Mathematical Modelling 4 — Questions and Answers
Question 1: A car rental company charges a flat fee of $25 plus $0.15 per mile. Which equation models the total cost C for m miles?
- C = 25m + 0.15
- C = 0.15m + 25 (Correct answer)
- C = 25 + 15m
- C = 0.15 + 25m
Correct answer: C = 0.15m + 25
The flat fee is a constant ($25) and the per-mile charge is variable, giving C = 0.15m + 25.
Question 2: A population of bacteria doubles every 3 hours. If the initial population is 500, what is the population after 9 hours?
- 1500
- 2000
- 4000 (Correct answer)
- 8000
Correct answer: 4000
After 9 hours there are 9/3 = 3 doubling periods, so population = 500 × 2³ = 4000.
Question 3: A water tank holds 800 gallons and drains at 40 gallons per hour. Which inequality represents when the tank has more than 200 gallons remaining?
- 800 − 40t > 200 (Correct answer)
- 800 + 40t > 200
- 40t − 800 > 200
- 800 − 40t < 200
Correct answer: 800 − 40t > 200
The remaining volume is 800 − 40t and it must exceed 200, giving 800 − 40t > 200.
Question 4: A projectile is launched upward with height modeled by h(t) = −16t² + 64t + 5. What is the maximum height reached?
- 64 ft
- 69 ft (Correct answer)
- 70 ft
- 80 ft
Correct answer: 69 ft
The vertex occurs at t = −64/(2×−16) = 2; h(2) = −16(4) + 64(2) + 5 = −64 + 128 + 5 = 69 ft.
Question 5: A store marks up wholesale prices by 40% and then applies a 10% discount for members. If the wholesale price is $50, what is the member price?
- $58.00
- $63.00 (Correct answer)
- $65.00
- $68.00
Correct answer: $63.00
Marked-up price = $50 × 1.40 = $70; member price = $70 × 0.90 = $63.
Question 6: Two cyclists start at the same point and travel in opposite directions. One rides at 12 mph and the other at 16 mph. How many hours until they are 84 miles apart?
- 2.5 h
- 3 h (Correct answer)
- 3.5 h
- 4 h
Correct answer: 3 h
Their combined speed is 12 + 16 = 28 mph; time = 84 ÷ 28 = 3 hours.
Question 7: A graph shows a linear relationship between the number of items produced (x) and total cost (y). The line passes through (0, 200) and (10, 700). What does the slope represent?
- The fixed cost per batch
- The cost of producing each additional item (Correct answer)
- The total number of items
- The revenue per item
Correct answer: The cost of producing each additional item
Slope = (700 − 200)/(10 − 0) = 50, which is the variable cost — the additional cost for each item produced.
NBT NBT Mathematical Modelling 4
A car rental company charges a flat fee of $25 plus $0.15 per mile.
Which equation models the total cost C for m miles?