11.6 Exponential and Logarithmic Functions

Objectifs d'apprentissage

Exponential 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.

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.