Developing Mathematical Models — Solutions

1. Identifying Variables

   1. Petrol scenario — Independent (x): distance driven ▶ View Solution   Dependent (y): petrol used ▶ View Solution
   2. Apples scenario — Independent (x): number of apples ▶ View Solution   Dependent (y): total cost ▶ View Solution

2. Reading a Table of Values

   1. Table: 12, 24, 36, 48 ▶ View Solution
   2. 8 minutes: 96 m² ▶ View Solution
   3. y = 12x ▶ View Solution

3. Formula Evaluation

   1. y = 11 ▶ View Solution
   2. y = 23 ▶ View Solution
   3. y = 3 ▶ View Solution

4. Writing a Formula from Words

   1. Independent variable: kilometres (k) ▶ View Solution
   2. Dependent variable: total cost (C) ▶ View Solution
   3. C = 2.50k + 3 ▶ View Solution
   4. 6 km trip: $18 ▶ View Solution

5. Speed and Distance

   1. Table: 15, 30, 45, 60 ▶ View Solution
   2. y = 15x ▶ View Solution
   3. 5.5 hours: 82.5 km ▶ View Solution

6. Two-Step Model: Delivery Fee

   1. C = 2.50k + 5 ▶ View Solution
   2. Table: $5, $10, $15, $20 ▶ View Solution
   3. 10 km: $30 ▶ View Solution

7. Decreasing Model: Water Tank

   1. Table: 200, 192, 184, 176 ▶ View Solution
   2. y = 200 − 8x ▶ View Solution
   3. 15 minutes: 80 litres ▶ View Solution

8. Finding a Formula from a Sequence

   1. (1, 5)   (2, 9)   (3, 13)   (4, 17) ▶ View Solution
   2. Common difference: 4 ▶ View Solution
   3. y = 4x + 1 ▶ View Solution
   4. 25th term: 101 ▶ View Solution

9. Solving Backwards: Electrician's Bill

   1. C = 55h + 75 ▶ View Solution
   2. 4-hour job: $295 ▶ View Solution
   3. $405 bill: 6 hours ▶ View Solution
   4. Max $600: 9 whole hours ▶ View Solution

10. Comparing Two Plans

    1. Formulas: Tutor A: C = 45h    Tutor B: C = 30h + 30 ▶ View Solution
    2. 3-hour session: Tutor A: $135    Tutor B: $120 ▶ View Solution
    3. Same cost at: 2 hours ▶ View Solution