11.6 Exponential and Logarithmic Functions
Term 2
Exponential shape and asymptote · Growth and decay · Depreciation and compound interest · Contextual meaning of parameters · [EXT] Index laws for rational indices · [EXT] Introduction to logarithms, log laws and log equations
Learning Objectives
PrintExponential Functions
- 1. Understand the shape of an exponential function $y = a \cdot b^x$ and identify key intercepts and the horizontal asymptote.
- 2. Explore exponential graph transformations (vertical shift, reflection, dilation).
- 3. Solve real-life problems involving exponential growth and decay.
- 4. Solve depreciation and compound-interest problems.
- 5. Interpret the contextual meaning of the parameters $a$ and $b$ in $y = a \cdot b^x$.
- 6. Use technology to solve basic exponential equations.
Indices and Logarithms (Extended)
- 7. Apply index laws for rational indices, including $a^{m/n} = \sqrt[n]{a^m}$.
- 8. Convert between exponential and logarithmic form: $a^x = y \Leftrightarrow \log_a y = x$.
- 9. Apply the logarithm laws: product, quotient and power.
- 10. Solve logarithmic and exponential equations algebraically.
Review Pack
Open review hub
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)