Linear Explicit Rules and Tree Growth

The video tutorial explains how to construct a linear explicit rule for a scenario where a tree grows by 2 inches every year, starting at 36 inches. It introduces the formula F(n) = F(1) + d * (n - 1), where F(1) is the initial value and d is the common difference. The tutorial walks through understanding and applying this formula to derive the equation F(n) = 36 + 2 * (n - 1).

What is the initial height of the tree?

• 40 inches

• 36 inches

• 38 inches

• 34 inches

Which form does a linear explicit rule follow?

• F(n) = F(1) - d * (n - 1)

• F(n) = F(1) * d * n

• F(n) = F(1) + d * (n - 1)

• F(n) = F(1) + d * n

In the context of the tree's growth, what does the 'd' represent?

• The initial height

• The number of years

• The total height

• The growth per year

What is the starting value in the linear explicit rule for the tree?

• n

• F(n)

• 2

• 36

How is the common difference used in the linear explicit rule?

• It is added to the starting value

• It is multiplied by (n - 1)

• It is subtracted from the starting value

• It is divided by n

What is the final linear explicit rule for the tree's growth?

• F(n) = 36 + 2 * n

• F(n) = 36 - 2 * (n - 1)

• F(n) = 36 + 2 * (n - 1)

• F(n) = 36 * 2 * (n - 1)

What does the term 'n - 1' signify in the linear explicit rule?

• The number of years

• The common difference

• The term number minus one

• The initial height