Practice question · Sort into groups
Sort these into growth models vs decay models.
Groups: Growth () · Decay ()
- Radioactive decay
- Population with positive birth rate
- Asset depreciation
- Viral spread in early phase
- Continuous compound interest at 5%
- Brand awareness without advertising
Hints
- The sign of the rate constant decides the category.
- Anything wearing away or fading belongs to the second group.
Show the answer
Growth (): Continuous compound interest at 5%, Population with positive birth rate, Viral spread in early phase
Decay (): Radioactive decay, Brand awareness without advertising, Asset depreciation
Why
Interest, population, and viral spread grow; decay, awareness loss, and depreciation shrink. The sign of tells the story.
Practise First-Order Differential Equations
The app has 5 more questions on this lesson, and keeps your place in the course. Business I is free to start.
More questions on First-Order Differential Equations
- y = y0 e^kt solves doty = ky because the exponential is its own derivative up to a constant.
- At 7% continuous growth, the Rule of 70 says doubling time is roughly 70/7 = 10 years. Estimate e⁰.7.
- An exponential decay model stays accurate all the way down to the last few units of the quantity.
- Which spreadsheet formula computes continuous compound interest A = 1000 × e⁰.05 × 10?
- Half-life from a decay rate k is computed as ln 2 / |k| rather than 2/k. Why does a logarithm appear?
- Match each ODE to its economic model.
- A separable differential equation and a non-separable one may describe equally simple business situations.…