Practice question · True or false
An exponential decay model stays accurate all the way down to the last few units of the quantity.
Hints
- What does the model assume about the population?
- Averages stop working when the numbers get small.
Show the answer
False
Why
False. Exponential decay is a continuous average over many units; once few remain, individual randomness dominates and the smooth curve stops describing anything. The model never reaches zero mathematically, and the real quantity does, the mismatch is a sign of leaving the model's domain.
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
- Sort these into growth models vs decay models.
- 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.
- 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.…