Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u03-l06', 'number': 6, 'title': 'Logarithmic Scales and Data Interpretation', 'family': 'logarithmic', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Rewrite log₂32=5 in exponential form.
2. {'id': 'u03-l06', 'number': 6, 'title': 'Logarithmic Scales and Data Interpretation', 'family': 'logarithmic', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Evaluate log₁₀0.001.
3. {'id': 'u03-l06', 'number': 6, 'title': 'Logarithmic Scales and Data Interpretation', 'family': 'logarithmic', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Expand ln(3x²).
4. {'id': 'u03-l06', 'number': 6, 'title': 'Logarithmic Scales and Data Interpretation', 'family': 'logarithmic', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Condense 2lnx−ln(x+1).
5. {'id': 'u03-l06', 'number': 6, 'title': 'Logarithmic Scales and Data Interpretation', 'family': 'logarithmic', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Solve log₃(x−1)=2.
6. {'id': 'u03-l06', 'number': 6, 'title': 'Logarithmic Scales and Data Interpretation', 'family': 'logarithmic', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Use change of base to express log₇20.
7. {'id': 'u03-l07', 'number': 7, 'title': 'Exponential Regression and Model Validation', 'family': 'exponential', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
A quantity begins at 500 and grows 4% yearly. Write the model.
8. {'id': 'u03-l07', 'number': 7, 'title': 'Exponential Regression and Model Validation', 'family': 'exponential', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Evaluate 200(0.8)^3.
9. {'id': 'u03-l07', 'number': 7, 'title': 'Exponential Regression and Model Validation', 'family': 'exponential', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
A population doubles every 6 years. Give a base-2 model.
10. {'id': 'u03-l07', 'number': 7, 'title': 'Exponential Regression and Model Validation', 'family': 'exponential', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Solve 3^x=81.
11. {'id': 'u03-l07', 'number': 7, 'title': 'Exponential Regression and Model Validation', 'family': 'exponential', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Find the continuous growth rate k if A=A₀e^{0.07t}.
12. {'id': 'u03-l07', 'number': 7, 'title': 'Exponential Regression and Model Validation', 'family': 'exponential', 'week': 9, 'unit': 3, 'unit_title': 'Exponential & Logarithmic Functions', 'essential': 'How do multiplicative change, inverse structure, logarithmic scales, and parameter interpretation support defensible growth and decay models?', 'project': 'Growth, Decay & Scale Modelling Report'}
Find the half-life for A=A₀e^{-0.2t}.