the table represents the height of a roller coaster, ( h(t) ), in meters, ( t ) seconds after the roller…

the table represents the height of a roller coaster, ( h(t) ), in meters, ( t ) seconds after the roller coaster starts moving.\n\nwhat is the average rate of change of the roller coaster over the interval from ( t = 6 ) seconds to ( t = 18 ) seconds?\n- 60 meters per second\n- 45 meters per second\n- 30 meters per second\n- 5 meters per second

the table represents the height of a roller coaster, ( h(t) ), in meters, ( t ) seconds after the roller coaster starts moving.\n\nwhat is the average rate of change of the roller coaster over the interval from ( t = 6 ) seconds to ( t = 18 ) seconds?\n- 60 meters per second\n- 45 meters per second\n- 30 meters per second\n- 5 meters per second

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) over the interval ([x_1,x_2]) is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}). Here, (x=t), (y = H(t)), (x_1 = 6), (x_2=18), (H(x_1)=H(6) = 75), (H(x_2)=H(18)=15).

Step2: Substitute the values into the formula

[ \begin{align*} \frac{H(18)-H(6)}{18 - 6}&=\frac{15-75}{18 - 6}\ &=\frac{-60}{12}\ \end{align*} ]

Step3: Simplify the expression

(\frac{-60}{12}=- 5)

Answer:

-5 meters per second