Question
Two housing developments are building homes.
Development Description
The number of homes built increases by 15% per year.
The number of homes built increases by 15% per year.
Which statement is true?
Responses
The descriptions for both housing developments are best modeled by exponential functions.
The descriptions for both housing developments are best modeled by exponential functions.
The descriptions for both housing developments are best modeled by linear functions.
The descriptions for both housing developments are best modeled by linear functions.
The description for Development is best modeled by a linear function, while the description for Development is best modeled by an exponential function.
The description for Development 1 is best modeled by a linear function, while the description for Development 2 is best modeled by an exponential function.
The description for Development is best modeled by an exponential function, while the description for Development is best modeled by a linear function.
The description for Development 1 is best modeled by an exponential function, while the description for Development 2 is best modeled by a linear function.
Development Description
The number of homes built increases by 15% per year.
The number of homes built increases by 15% per year.
Which statement is true?
Responses
The descriptions for both housing developments are best modeled by exponential functions.
The descriptions for both housing developments are best modeled by exponential functions.
The descriptions for both housing developments are best modeled by linear functions.
The descriptions for both housing developments are best modeled by linear functions.
The description for Development is best modeled by a linear function, while the description for Development is best modeled by an exponential function.
The description for Development 1 is best modeled by a linear function, while the description for Development 2 is best modeled by an exponential function.
The description for Development is best modeled by an exponential function, while the description for Development is best modeled by a linear function.
The description for Development 1 is best modeled by an exponential function, while the description for Development 2 is best modeled by a linear function.
Answers
GPT-4o mini
Given that both housing developments increase the number of homes built by 15% per year, the correct conclusion is:
**The descriptions for both housing developments are best modeled by exponential functions.**
This is because an increase of a fixed percentage over time results in exponential growth rather than linear growth. In exponential functions, the growth rate is proportional to the current amount, meaning as the number of homes increases, the amount added each year also increases.
**The descriptions for both housing developments are best modeled by exponential functions.**
This is because an increase of a fixed percentage over time results in exponential growth rather than linear growth. In exponential functions, the growth rate is proportional to the current amount, meaning as the number of homes increases, the amount added each year also increases.