AC9M10A04 Year 10 Mathematics

Content descriptor use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; interpret solutions in terms of the situation; evaluate and modify models as necessary and report assumptions, methods and findings

Elaborations

• • Elaboration modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable
• • Elaboration modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay; for example, situations involving constant percentage change and constant ratio; determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
• • Elaboration modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
• • Elaboration modelling and investigating how exponential equations are used in carbon dating to estimate the age of First Nations Australians’ artefacts or material culture
• • Elaboration modelling and formulating situations involving population growths of native animals on Country/Place with varying reproductive behaviour, using exponential equations and critiquing their applicability to real-world situations