Question

1. which of the following scenarios would best be modeled by a continuous exponential growth or decay model? a) the number of rabbits in an australian meadow b) the number of people who hear a rumor at a school c) the temperature of a mug of hot chocolate as it cools d) the height of a basketball after each bounce

Explanation:

To determine which scenario is best modeled by a continuous exponential growth or decay model, we analyze each option:

• Option A: The number of rabbits is discrete (countable) and follows a discrete exponential growth model (like a geometric sequence) rather than continuous, as you can't have a fraction of a rabbit.
• Option B: The number of people hearing a rumor is discrete (you can't have a fraction of a person) and typically follows a logistic growth model (s - shaped curve) due to limited population, not a simple continuous exponential model.
• Option C: The temperature of a mug of hot chocolate cooling follows Newton's Law of Cooling, which is a continuous exponential decay model. The temperature changes continuously over time as it approaches the ambient temperature.
• Option D: The height of a basketball after each bounce is a discrete process (each bounce is a distinct event) and follows a geometric sequence (discrete decay) as the height after each bounce is a fraction of the previous height, but it's not continuous.

Answer:

C) The temperature of a mug of hot chocolate as it cools