Question

the equation ( h(t)=-16 t^{2}-7 t + 3000 ) gives the height of an object that was thrown downward at 7 feet/second at an initial height of 3000 feet. use this equation to find the average rate of change in height (average speed) of the ball from 3 to 4 seconds? give answer as an integer or reduced fraction. the average rate of change (average speed) = ( ) ft/s question help: message instructor submit question

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = h(t)\) over the interval \([a,b]\) is \(\frac{h(b)-h(a)}{b - a}\). Here, \(a = 3\), \(b=4\), and \(h(t)=-16t^{2}-7t + 3000\).

Step2: Calculate \(h(3)\)

Substitute \(t = 3\) into \(h(t)\):

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Step3: Calculate \(h(4)\)

Substitute \(t = 4\) into \(h(t)\):

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Step4: Calculate the average rate of change

Use the formula \(\frac{h(4)-h(3)}{4 - 3}\). Substitute \(h(3)=2835\) and \(h(4)=2716\) into it:

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Answer:

\(-119\)