Question

the height in feet, (h), of a model rocket (t) seconds after launch is given by the equation (h(t) = 3 + 70t - 16t^2). the average rate of change in (h(t)) between (t = 1) second and (t = 3) second is (6). what does the average rate of change tell you about the rocket?

• the rocket is traveling six times as fast when (t = 3) than it is when (t = 1)
• the rocket is at a greater height when (t = 3) than it is when (t = 1)
• the rocket is 6 feet higher above the ground when (t = 3) than it is when (t = 1)
• the rocket is traveling at a constant rate of 6 feet per second between (t = 1) and (t = 3)

Explanation:

Define average rate of change

$$ \text{Average Rate of Change} = \frac{h(3) - h(1)}{3 - 1} = 6 $$

Interpret the mathematical relationship

$$ \frac{h(3) - h(1)}{2} = 6 \implies h(3) - h(1) = 12 $$

Evaluate the given options

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Answer:

• The rocket is traveling six times as fast when \(t = 3\) than it is when \(t = 1\)
• The rocket is at a greater height when \(t = 3\) than it is when \(t = 1\) (Correct answer)
• The rocket is 6 feet higher above the ground when \(t = 3\) than it is when \(t = 1\)
• The rocket is traveling at a constant rate of 6 feet per second between \(t = 1\) and \(t = 3\)