Question

1. what kind of real-world application uses exponential decay models?

a. estimating construction costs over time

b. predicting traffic flow increase

c. calculating the half-life of a chemical substance

d. election polling analysis

Explanation:

• Option a: Construction costs over time are more likely to follow linear or other non - exponential decay models (or even growth in some cases), so this is not a typical exponential decay application.
• Option b: Predicting traffic flow increase is related to growth, not decay, so it does not use exponential decay models.
• Option c: The half - life of a chemical substance (especially radioactive substances) is a classic example of exponential decay. The amount of the substance remaining after a certain time follows the exponential decay formula $N(t)=N_0e^{-\lambda t}$ (or other equivalent exponential decay forms), where $N(t)$ is the amount at time $t$, $N_0$ is the initial amount, and $\lambda$ is the decay constant.
• Option d: Election polling analysis is related to sampling, probability of different outcomes, and is not based on exponential decay models.

Answer:

c. Calculating the half - life of a chemical substance