Question
A hot air balloon descends to the ground. The function h(t) = 210 - 15t can be used to describe the altitude of the
balloon as it approaches the ground. Which statement best describes the graph of the function that models the descent of the balloon?
The graph is discrete because there cannot be fractional values for time.
• The graph is discrete because there cannot be negative values for altitude.
• The graph is continuous because there can be fractional values for time.
• The graph is continuous because there can be negative values for altitude.
balloon as it approaches the ground. Which statement best describes the graph of the function that models the descent of the balloon?
The graph is discrete because there cannot be fractional values for time.
• The graph is discrete because there cannot be negative values for altitude.
• The graph is continuous because there can be fractional values for time.
• The graph is continuous because there can be negative values for altitude.
Answers
GPT-4o mini
The best statement that describes the graph of the function \( h(t) = 210 - 15t \) modeling the descent of the hot air balloon is:
**The graph is continuous because there can be fractional values for time.**
This is true because the function represents a continuous linear model where time \( t \) can take on any real value, including fractional values, as the hot air balloon descends. Altitude can also take on a variety of values, but the important point here is that time is continuous. The altitude, \( h(t) \), will eventually reach zero and can go negative in a mathematical sense but in a physical context, we interpret it as the balloon being on the ground or below it.
**The graph is continuous because there can be fractional values for time.**
This is true because the function represents a continuous linear model where time \( t \) can take on any real value, including fractional values, as the hot air balloon descends. Altitude can also take on a variety of values, but the important point here is that time is continuous. The altitude, \( h(t) \), will eventually reach zero and can go negative in a mathematical sense but in a physical context, we interpret it as the balloon being on the ground or below it.