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.

Answer 1

Ans: Option (C) The graph is continuous because there can be fractional values for time.

Step-by-step explanation:
Time is a continuous quantity. For example: you can express time in microseconds, nanoseconds, picoseconds and so on and so forth. In other words, the time can be 0.001s or 1s or 10s etc. The point I am trying to make here is that the time can take infinite amount of numbers. Therefore, the given function:

h(t) = 210 - 15t

will have the continuous graph because the time is a continuous quantity, not a discrete quantity, and accept the fractional values as well.

For example:
h(0) = 210
(In between there are infinite numbers for time to be substituted in h(t))
h(0.0000001) = 210-15(0.0000001)
as so on.

and the graph of the given function will be continuous.

Hence the correct option is (C) The graph is continuous because there can be fractional values for time.

Answer 2

Answer – C. (The graph is continuous because there can be fractional values for time) First we must understand that there can be fractional values for time; time can take on any value value within a finite or infinite interval, and as such is a continuous variable. Therefore, the graph is continuous.