Modeling Tree Branch Growth

The video tutorial explores how to model the growth of branches in oak and birch trees using mathematical functions. It begins by presenting data on the number of branches over time for both trees. The oak tree data is analyzed using a linear model due to its relatively constant increase in branches every three years. In contrast, the birch tree data is better suited to an exponential model, as the number of branches multiplies by a factor of four every decade. The video demonstrates how to construct these models and verify their accuracy with the given data.

What are the two types of functions considered for modeling the tree data?

• Exponential and logarithmic

• Quadratic and cubic

• Linear and exponential

• Linear and quadratic

What is the key factor in deciding between a linear and exponential model?

• The fixed increase in time

• The average number of branches

• The multiplication factor

• The initial number of branches

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CCSS.HSF-LE.A.1B

What is the average increase in branches for the oak tree over three years?

• 20 branches

• 10 branches

• 12 branches

• 15 branches

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CCSS.HSF.BF.A.2

How many branches does the oak tree have at the start?

• 70 branches

• 59 branches

• 46 branches

• 34 branches

What type of model is used for the oak tree?

• Logarithmic

• Exponential

• Linear

• Quadratic

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CCSS.HSF.BF.A.2

What is the multiplication factor for the birch tree's branch growth every 10 years?

• 2

• 3

• 4

• 5

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CCSS.HSF.BF.A.2

How many branches does the birch tree have initially?

• 8 branches

• 33 branches

• 512 branches

• 128 branches

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CCSS.HSF.LE.A.2

What is the exponential model's initial condition for the birch tree?

• 32 branches

• 16 branches

• 8 branches

• 4 branches

How many branches does the birch tree have after 30 years according to the model?

• 1024 branches

• 512 branches

• 256 branches

• 128 branches

What is the main characteristic of the birch tree's growth pattern?

• Random growth

• Decreasing growth

• Constant multiplication

• Constant addition