Practice question · Multiple choice
Half-life from a decay rate is computed as rather than . Why does a logarithm appear?
Hints
- Write and solve for .
- What operation undoes an exponential?
Show the answer
A. Because halving is reached after a fixed multiple of
Why
The logarithm is what inverts the exponential. It is also why half-life is constant: the time to halve does not depend on where you start, which is peculiar to exponential decay.
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.
- 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?
- Match each ODE to its economic model.
- A separable differential equation and a non-separable one may describe equally simple business situations.…