Question
There are 1000 lions in the wild.Each year the number is halved. Is this linear or exponential?
Answers
GPT-4o mini
The situation you've described, where the number of lions is halved each year, represents an **exponential decay** rather than a linear decline.
In a linear decrease, the quantity decreases by a constant amount each time period. For example, if you had 1000 lions and lost 100 each year, you would have:
- Year 1: 900
- Year 2: 800
- Year 3: 700
In contrast, in exponential decay, the quantity decreases by a constant proportion. In your example, the number of lions is halved each year:
- Year 1: 1000 / 2 = 500
- Year 2: 500 / 2 = 250
- Year 3: 250 / 2 = 125
This results in a rapid initial decline that slows over time, characteristic of exponential functions. Therefore, the halving of the lion population each year is an example of exponential decay.
In a linear decrease, the quantity decreases by a constant amount each time period. For example, if you had 1000 lions and lost 100 each year, you would have:
- Year 1: 900
- Year 2: 800
- Year 3: 700
In contrast, in exponential decay, the quantity decreases by a constant proportion. In your example, the number of lions is halved each year:
- Year 1: 1000 / 2 = 500
- Year 2: 500 / 2 = 250
- Year 3: 250 / 2 = 125
This results in a rapid initial decline that slows over time, characteristic of exponential functions. Therefore, the halving of the lion population each year is an example of exponential decay.