Calculus · Week 31 · Differential Equations
Exponential Growth and Decay
When a quantity changes at a rate proportional to its size, dy/dt = ky leads to y = y0 e^(kt), and the given facts decide which model fits.
- Students will
- Students solve dy/dt = ky with an initial condition and use the given facts to find k and predict a future value.
- SEL skill
- Decide whether a model shows growth or decay and which fact finds k before computing
- What it looks like
- Students practice responsible decision-making by deciding, with a partner, which given fact finds k and whether the model shows growth or decay before computing.
- Content focus
- Exponential models from dy/dt = ky
- Format
- Collaborative analysis
Responsible decision-making
Responsible decision-making means making careful, caring choices, which in math starts with deciding what the given facts tell you before you act. More responsible decision-making activities
What you get
A teacher guide with what to say, step by step, plus student pages and a supports page for students with diverse learning needs, including those with IEPs. Print or Project it, or assign it in Google Forms and Google Docs for Google Classroom. Your first 10 activities are free.
Standards
- AB 7.8: AP Calculus AB, Unit 7, Topic 7.8
- Standard for Mathematical Practice: MP4 Model with mathematics
- CA Mathematics Framework (2023): Exploring Changing Quantities
- Traditional course: Calculus
More responsible decision-making activities for Calculus
- Continuity and the Intermediate Value Theorem Responsible decision-makingChecking continuity, fixing removable discontinuities, and deciding when the Intermediate Value Theorem applies.
- Inverse Functions and Their Derivatives Responsible decision-makingChoosing between the inverse derivative rule and inverse trig formulas, and explaining the choice.
- Choosing the Right Rule Responsible decision-makingReading how a function is built before choosing a derivative rule.
- Close Enough? Local Linear Approximation Responsible decision-makingUsing a tangent line to estimate and deciding whether to trust it.
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