Question
Which one of the following scenarios can be modeled by an exponential function the total pay of a person who earns $15 per hour a population of bacteria that doubles every hour of population of bacteria that increases by 10 every hour the total pay of a person who earns a different rate depending on the job
Answers
GPT-4o mini
The scenario that can be modeled by an exponential function is:
- **A population of bacteria that doubles every hour.**
In this case, the population grows by a constant multiplicative factor (in this instance, it doubles, which is a factor of 2) at regular intervals (every hour). This is characteristic of exponential growth.
The other scenarios are better modeled by linear functions or other types of functions:
- The total pay of a person who earns $15 per hour is linear, as it increases by a constant amount each hour (a fixed rate).
- A population of bacteria that increases by 10 every hour is also linear, as it adds a fixed amount each hour.
- The total pay of a person who earns a different rate depending on the job does not follow a consistent pattern to be modeled by a single function type, making it outside the realm of simple exponential growth or decay.
Thus, the only exponential function scenario is the population of bacteria that doubles every hour.
- **A population of bacteria that doubles every hour.**
In this case, the population grows by a constant multiplicative factor (in this instance, it doubles, which is a factor of 2) at regular intervals (every hour). This is characteristic of exponential growth.
The other scenarios are better modeled by linear functions or other types of functions:
- The total pay of a person who earns $15 per hour is linear, as it increases by a constant amount each hour (a fixed rate).
- A population of bacteria that increases by 10 every hour is also linear, as it adds a fixed amount each hour.
- The total pay of a person who earns a different rate depending on the job does not follow a consistent pattern to be modeled by a single function type, making it outside the realm of simple exponential growth or decay.
Thus, the only exponential function scenario is the population of bacteria that doubles every hour.