Family and learning-support guide

Exponential Functions & Growth Models

How do repeated multiplication, percent change, and continuous growth create exponential patterns and decisions?

What the learner will study

  • Exponential Function Structure & Parameters
  • Growth, Decay & Percent Change
  • Compound Interest & Effective Rates
  • Continuous Growth, Decay & the Constant e
  • Solving Exponential Equations by Common Bases
  • Exponential Regression & Data Modelling
  • Comparing Linear, Quadratic & Exponential Models

How to support without taking over

  • Ask the learner to define inputs, outputs, units, and domain.
  • Ask which property or theorem justifies each transformation.
  • Request an independent check by substitution, graph, table, or alternate method.
  • Encourage correction notes rather than erasing evidence of learning.
  • Use the calculator after the mathematical setup is visible.

Evidence to preserve

Keep one worked example, one correction, one application or project artifact, the mastery result, and a reflection explaining growth and next steps.

Applied investigation

Exponential Growth, Decay & Financial Scenario Audit asks the learner to define a real question, construct mathematics, validate results, state uncertainty, and communicate a defensible conclusion.

Open Investigation