Linear, quadratic and financial modelling

A taxi charges $5 plus $2 per kilometre. Write a linear model for the cost.

For C = 5 + 2d, find C when d = 12.

A savings account starts with $200 and gains $30 per month. Write a linear model.

Calculate simple interest on $500 at 4% per year for 3 years.

Explain the difference between a linear model and a quadratic model.

Identify the fixed cost and variable cost in C = 40 + 12n.

A rectangle has area A = x(20 - x). Explain why this is quadratic.

State one limitation of using a mathematical model.

Correct this error: a $100 item with 20% discount costs $20.

Give one example of a financial decision that can be modelled mathematically.

Compare two phone plans: Plan A costs $20 plus $4 per GB, Plan B costs $50 plus $1 per GB. Find the break-even point and interpret it.

A concert ticket company charges a booking fee plus a price per ticket. Create a linear model and use it to answer two questions.

Calculate the simple interest and final value for an investment of $1200 at 5% per year for 4 years.

Model the area of a rectangular enclosure with fixed perimeter 40 m. Explain why the area relation is quadratic.

A shop gives a 30% discount and then adds 10% GST. Find the final price of a $200 item and explain the order.

Compare a linear cost model and a quadratic area model. Explain what each type of model is useful for.

Create a table and graph description for a financial model, identifying the intercept and gradient.

Evaluate a model that assumes prices, rates or conditions never change. Explain the limitation.

Solve a practical modelling problem where choosing the best option depends on usage amount.

Write a full response modelling a real financial or measurement situation, including equation, calculation, interpretation and limitation.