Full unit practice requiring complete reasoning and representation checks.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u03-l01', 'number': 1, 'title': 'Exponential Growth, Decay & Percent Change', 'family': 'exponential', 'week': 7, '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.
2. {'id': 'u03-l01', 'number': 1, 'title': 'Exponential Growth, Decay & Percent Change', 'family': 'exponential', 'week': 7, '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.
3. {'id': 'u03-l01', 'number': 1, 'title': 'Exponential Growth, Decay & Percent Change', 'family': 'exponential', 'week': 7, '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.
4. {'id': 'u03-l01', 'number': 1, 'title': 'Exponential Growth, Decay & Percent Change', 'family': 'exponential', 'week': 7, '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.
5. {'id': 'u03-l01', 'number': 1, 'title': 'Exponential Growth, Decay & Percent Change', 'family': 'exponential', 'week': 7, '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}.
6. {'id': 'u03-l01', 'number': 1, 'title': 'Exponential Growth, Decay & Percent Change', 'family': 'exponential', 'week': 7, '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}.
7. {'id': 'u03-l02', 'number': 2, 'title': 'The Number e and Continuous Change', 'family': 'exponential', 'week': 7, '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-l02', 'number': 2, 'title': 'The Number e and Continuous Change', 'family': 'exponential', 'week': 7, '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-l02', 'number': 2, 'title': 'The Number e and Continuous Change', 'family': 'exponential', 'week': 7, '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-l02', 'number': 2, 'title': 'The Number e and Continuous Change', 'family': 'exponential', 'week': 7, '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-l02', 'number': 2, 'title': 'The Number e and Continuous Change', 'family': 'exponential', 'week': 7, '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-l02', 'number': 2, 'title': 'The Number e and Continuous Change', 'family': 'exponential', 'week': 7, '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}.