📊 Part 1: Understanding Linear Financial Models

1. A mobile phone plan costs $25 per month plus $2 for each gigabyte of data used. Which equation represents the total monthly cost (C) for using d gigabytes?

C = 25d + 2

C = 25 + 2d

C = 27d

C = 2d - 25

2. In the equation C = 40 + 15n, where C is total cost and n is number of items, what does the number 40 represent?

Cost per item

Fixed cost

Total number of items

Variable cost

3. Which of the following are characteristics of linear financial models? (Select all that apply)

Constant rate of change

Straight line when graphed

Contains a fixed cost component

Always starts at zero

4. A catering company charges $150 venue hire plus $35 per person. If the total cost is $780, how many people attended?

15 people

18 people

20 people

22 people

📈 Part 2: Creating and Interpreting Models

5. Sarah wants to start a small business selling handmade jewellery. She has fixed costs of $200 per month (rent, insurance) and each piece of jewellery costs $8 to make. She sells each piece for $25.

a) Write an equation for her total monthly costs (C) if she makes n pieces of jewellery:

C = ________________

b) Write an equation for her total monthly revenue (R) if she sells n pieces of jewellery:

R = ________________

c) How many pieces must she sell to break even? Show your working:

6. A gym membership costs $45 to join plus $30 per month. Complete the table below:

Months (m)	0	1	3	6	12
Total Cost ($)	____	____	____	____	____

7. In the gym membership scenario above, what does the slope of the line represent in real-world terms?

🔍 Part 3: Evaluating Financial Models

8. A taxi company charges $4.50 for the first kilometre and $2.20 for each additional kilometre. The linear model is: Cost = 4.50 + 2.20(k-1), where k is total kilometres travelled.

a) Calculate the cost for a 7km trip:

b) List two assumptions this linear model makes about taxi pricing that might not be realistic:

9. Explain why linear models are useful for financial planning, even when they may not be perfectly accurate:

10. Create your own linear financial model: Choose a real-world situation (e.g., party planning, car rental, subscription service) and write the equation, identifying the fixed and variable costs:

Situation: _________________________________________________

Fixed cost: $_______ Variable cost per unit: $_______ per _______

Linear equation: _________________________________________________