A balloon rising at a constant rate will rise farther in 60 seconds than in 45 seconds. which inequality shows this in function notation?
A. rate(45) > rate(60)
B height increase(60) > height increase(45)
C. rate(60) > rate(45)
D. height increase(45) > height increase (60)
D. height increase(45) > height increase (60)
B. height increase(60) > height increase(45)
To find the correct inequality, we need to understand the relation between the rate of the balloon and the time it takes for the balloon to rise. Let's break it down step by step:
1. First, we need to determine the relationship between rate and time. Since the balloon is rising at a constant rate, the rate remains the same throughout its ascent.
2. The distance the balloon travels is directly proportional to the time it takes. This means that a longer time will result in a greater distance.
3. Now, let's look at the options:
A. rate(45) > rate(60): This option compares the rates at 45 seconds and 60 seconds. However, the problem states that the rate remains constant, so the rates at different times should be the same. This option is not correct.
B. height increase(60) > height increase(45): This option compares the height increases at 60 seconds and 45 seconds. Since a longer time results in a greater distance, this option correctly expresses the relationship between the two heights. Therefore, this option is the correct answer.
C. rate(60) > rate(45): As discussed above, the rate remains constant throughout the balloon's ascent. So, the rates at 60 seconds and 45 seconds should be the same. This option is not correct.
D. height increase(45) > height increase(60): This option compares the height increases at 45 seconds and 60 seconds. However, we know that a longer time results in a greater distance, so this option does not accurately represent the relation between the two heights. This option is not correct.
Therefore, the correct inequality in function notation is: B. height increase(60) > height increase(45).