Section B Section B Checkpoint

Problem 1

A pattern of squares grows based on the expression $10n^2$ , where $n$ represents the step of the pattern.

A pattern of dots grows based on the expression $3^n$ , where $n$ represents the step of the pattern.

Han says that even though he doesn’t know which step it happens on, he knows that after some step, there will always be more dots than squares after that step. Do you agree or disagree? Explain your reasoning.

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Solution

I agree. Sample reasoning: The squares grow in a quadratic pattern, and the factor of growth between each step decreases (becomes closer and closer to 1) after each step. The dots grow based on an exponential pattern, and the factor of growth is always 3.

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Sample Response

Problem 2

A fall festival's pumpkin launcher sends pumpkins into the air so that the pumpkin's height in meters above the ground is modeled by the equation $h(t) = \text{-}5t^2 + 100t$ with $t$ as the time in seconds after launch.

A graph comparing the height above the ground in meters and the time in seconds. The x intercepts of the graph are at x=0 and x=20.

At what height above the ground was the pumpkin when it was launched?
What does the $100t$ in the equation mean in terms of the pumpkin?
About when does the pumpkin hit the ground?

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Solution

0 meters
It means that the pumpkin was initially launched at 100 meters per second.
20 seconds after the launch

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Sample Response

0 meters
It means that the pumpkin was initially launched at 100 meters per second.
20 seconds after the launch