This worksheet applies mathematical modelling to real growth and decay problems, including financial contexts, teaching students to choose between linear, quadratic and exponential models and evaluate their predictions. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A linear model (y=mx+c) fits change by a fixed amount each step — e.g. simple interest, straight-line depreciation.
- An exponential model (y=A×bˣ) fits change by a fixed percentage each step — e.g. compound interest, population growth, radioactive decay.
- A quadratic model (y=ax²+bx+c) fits situations with a turning point — e.g. projectile height over time.
- Simple interest: I=P×r×t (interest only). Compound interest: A=P×(1+r)ᵗ (total amount, interest earns interest).
- Every model should be evaluated for realism — e.g. a linear depreciation model eventually predicts a negative value, which doesn't make sense in reality, while exponential decay always stays positive.
What your child will practise:
- Identifying whether a growth/decay scenario is best modelled as linear, quadratic or exponential, based on how the quantity changes.
- Calculating simple interest and compare it with compound interest over the same period.
- Applying an exponential growth or decay model to a real context (population, depreciation, radioactive decay).
- Applying a quadratic model to a real context with a turning point (e.g. projectile motion) and find its maximum/zero.
- Evaluating a model's long-run prediction for realism and identify when a model should be modified.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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