AC9M10A04

See also: Learning Areas / Mathematics / Mathematics / Algebra / Year 10

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

• AC9M10A04_E1 - 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
• AC9M10A04_E2 - 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
• AC9M10A04_E3 - modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
• AC9M10A04_E4 - modelling and investigating how exponential equations are used in carbon dating to estimate the age of First Nations Australians’ artefacts or material culture
• AC9M10A04_E5 - 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

Achievement Standard Components

• ASMAT1002 - They use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying  linear,  quadratic and exponential functions as appropriate, and solve related equations, numerically and graphically.