7. the function h(t) shown in the graph above models the height over time of a * 1 point bottle rocket…

7. the function h(t) shown in the graph above models the height over time of a * 1 point bottle rocket launched from the roof of a house. which of the following statements is true? mark only one oval. the average rate of change in height of the bottle rocket from 0 to 0.5 seconds was less than the average rate from 1 to 1.5 seconds. the height of the rocket was decreasing over the interval 1.5 to 3.5 seconds. the average rate of change in height of the rocket from 1.5 to 2.5 seconds is about 5 meters per second. given the context, an appropriate domain for h(t) is all real numbers.

7. the function h(t) shown in the graph above models the height over time of a * 1 point bottle rocket launched from the roof of a house. which of the following statements is true? mark only one oval. the average rate of change in height of the bottle rocket from 0 to 0.5 seconds was less than the average rate from 1 to 1.5 seconds. the height of the rocket was decreasing over the interval 1.5 to 3.5 seconds. the average rate of change in height of the rocket from 1.5 to 2.5 seconds is about 5 meters per second. given the context, an appropriate domain for h(t) is all real numbers.

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = h(t)) over the interval ([a,b]) is (\frac{h(b)-h(a)}{b - a}).

Step2: Analyze the first option

For the interval ([0,0.5]): Let's assume (h(0)=0) (from the graph, at (t = 0) the height is (0)), and at (t=0.5), (h(0.5) = 14). The average rate of change is (\frac{14 - 0}{0.5-0}=\frac{14}{0.5}=28) For the interval ([1,1.5]): At (t = 1), (h(1)=18), at (t=1.5), (h(1.5)=19). The average rate of change is (\frac{19 - 18}{1.5 - 1}=\frac{1}{0.5}=2). So, the average rate of change from (0) to (0.5) is not less than from (1) to (1.5).

Step3: Analyze the second option

Looking at the graph, for (t\in[1.5,3.5]), as (t) increases, (h(t)) decreases.

Step4: Analyze the third option

For the interval ([1.5,2.5]): At (t = 1.5), (h(1.5)=19), at (t=2.5), (h(2.5)=16). The average rate of change is (\frac{16 - 19}{2.5 - 1.5}=\frac{- 3}{1}=-3\neq5)

Step5: Analyze the fourth option

The domain of (h(t)) (time) in the context of the bottle - rocket launch. Time (t\geq0) (we can't have negative time for the launch in this context), and the rocket lands at (t = 3.5). So, the domain is (0\leq t\leq3.5), not all real numbers.

Answer:

The height of the rocket was decreasing over the interval (1.5) to (3.5) seconds.